Pendulum Summoning is a Special Summoning mechanic introduced in the Arc-V era. Like Ritual Monsters, they reside in the main deck. However, after it gets removed from the field, they resides face-up in the Extra Deck. Despite having a series dedicated to this mechanic, Konami has since neglected it.

How to Pendulum Summon?

Mechanically, Pendulum Summoning is easy to learn. Once per turn, you can Special Summon monsters from your hand or face-up in your Extra deck between the two set scales. If a Pendulum leaves the field, they go to the Extra Deck allowing the players to summon them again. However, since Master Rule 4, the existence of the Extra Deck Zone hinders their recursion. Thematically, they are different from the other summon mechanics. 

Pros and Cons

On the surface level, pendulums sound powerful. You swarm the field quickly, easy to use, "splashable" (in theory) and they have amazing recovery. It's due to this that many people hate this mechanic. However, only a total of three Pendulum Archetypes (e.g. Qli, Metalfoes and Pepe) were ever meta relevant even back in MR3 when pendulums were at their prime.

This is due to the fragile nature of the mechanic. They die completely to summon negation. However, unlike other mechanics, this hurts pendulums because it's essentially having your field nuked. The mechanic is only once per turn. Therefore, stopping the initial Pendulum Summon hinders their pendulum combo. The mechanic is susceptible to more disruption, especially Spell/Trap removals (e.g. Twin Twister). Lack of hand advantage is a huge problem. Imagine starting a turn with five cards. Committing two cards to set up the scales leaves you now with three cards. Better hope the other cards in your hand are monsters or you won't be pendulum summoning and pray that they'll recover hand advantages. Ever since MR4, the scales now occupy two of the Spell/Trap Zones which limits the amount of spell/trap you can play.

The other problem with Pendulums is what they do well can also be done in other decks without the pendulums restrictions. Swarming the field isn't uncommon in modern Yu-Gi-Oh. Many decks can swarm the field quickly without committing two cards or having the once per turn restriction. Pendulums have great recursion (before MR4), but many modern decks can also recover cards from the Graveyard and Banish Zone easily.

However, despite its cons, some archetypes that have pendulum monsters often use their pendulum cards for their practical scale effects (e.g. Lunalight Tiger).  

Pendulum Archetypes

The most notable pendulum archetypes are Qli, Pepe and Metalfoes. The second one is so infamously powerful that Konami issued an emergency ban list to nerf it.

There are other notable pendulum decks like Pendulum Magicians, Magespectar, Igknight, Endymion and as of recently popular (due to the CAC Contest), Dinomist.

Qliphort

Qliphort is relatively consistent and robust. Scout and Saqlifice are great searchers. Their ability to recur their tribute fodders allow the deck to grind the opponent out. Most rogue decks don't have an out to Towers other than Kaiju. Their ability to run and bypass floodgates (e.g. Vanity's Emptiness and Skill Drain) really let the deck shine during its era.

On top of that, the archetype has decent card removal effects. Konami soon hit them by limiting their searchers which hurts their consistency and resilience. Since then, the archetype has come off the ban list but has fallen off the meta thanks to MR4, stronger and faster archetypes, hand traps, better Trap/Spell removals and better monster removals. 

PEPE

Pepe is the most infamous pendulum deck. What makes Pepe so powerful is how consistent the deck was. Almost all the card in the deck can be searched by cards like Pendulum Wizard, Joker, The Dracoslayers cards and Monkeyboard that results in convoluted combo plays with Ignister/Dinoster/Majester, Cyber Dragon Infinity and possibly up to four counter traps if running Ariadne. The other problem about them isn't the fact that they can search, but that they are also generating additional plusses with cards like Plushfire. Konami infamously hit them with an emergency ban list. Here's a video of what full power PEPE looks like:

https://www.youtube.com/watch?v=uopv_CUEwhY&ab_channel=CaptainChurrr

Metalfoes

Metalfoes was competitively successful during the era where the format was slower. Their ability to fill up their extra deck quickly and spam it out, and also their ability to be teched into other decks, as well as their consistency and ability to put out disruption were excellent during the slower meta. Since then, they have fallen off the meta thanks to MR4 and the existence of faster and stronger decks. Electrumite was a staple in many pendulum decks until Konami decided to hit it.

Master Rules 4

On March 25, 2017, Konami implemented Master Rule 4, which serve as a straight-up nerf to the pendulum mechanics. The introduction of the Extra Deck Zone and the rule of summoning only one extra deck monster on the field unless you have link monsters with arrows putting to available spot, hindered the mechanic's ability to recover their field and spam the field with monsters. On top of that, the combining of pendulum scales zone to normal spell/trap zone has also hindered the mechanic's ability to play more than three face-up continuous spell or trap cards.

On April 1, 2020, Master Rule 2020 saw a buff to all previous extra deck mechanic except pendulums. Pendulums' ability to recur and swarm the film is still being hindered as face-up extra Deck monsters cannot swarm the field unless link monsters open up the zones.

It's quite clear with Master Rule 4 and Master Rule 2020 that Konami is deliberately blocking the power of the pendulum mechanic.

Why is Konami neglecting Pendulum?

Why is Konami neglecting Pendulum? There weren't many pendulums released during the Vrains era, and it seems like Konami is deliberately avoiding buffing the mechanic despite the mechanic not dominating since the Arc-V era.

Hard to Balance

Like Rituals, Pendulums are difficult to balance. Due to the glass cannon nature of the mechanic, they'll either be very good or very bad. It's also isn't easy addressing their weaknesses.

For example, the mechanic lacks consistency, so to counter that, you would give searchers that searches its key pieces. The key pieces would then theoretically allow the mechanic to summon powerful monsters from hand and recur them. Therefore, to prevent this from happening, what do you do? You can give the monsters awkward levels (early Performapals) so they can't be spam out so easily which defeats the purpose of the searchers.

However, giving monsters gimmicky restrictions usually results in minus. Another method is by making the monsters weak, which makes them glorified extra deck fodders. This then leads to the spamming of the materials repeatedly. Konami realized this as many late tuner pendulum monsters have restrictions that hurt its ability to recur. This then makes you wonder why Konami bothered making them pendulum in the first place.

This design philosophy has plagued many pendulum decks. Abyss Actor has some destructive effect and some OTK plays, but they brick easily due to the lack of consistency and awkward levelling/scales. Amorphage has some nasty floodgate effects, but they again lack consistency combined with awkward levels and scales, and their gimmick of destroying itself means they're relatively resourced heavy. Then you have Majespecter, which is a very consistent archetype, and Kirin is a powerful card, they also have decent protection effect, but they have weak attack power. Their gameplay hinders them from going extra deck plays, or they lose card advantage.

Doesn't fit Konami's vision?

Pendulum summoning ironically doesn't fit into Konami's design philosophy. Based on how Konami designs their archetype, they love creating boss monsters for archetypes. Many summoning mechanics support this design philosophy where players use their Deck to Ritual/Fusion/Synchro/Xyz/link their boss monster. Pendulum summon's gameplay of spamming out monsters clashes with this design philosophy. Konami tries to remedy this by having the spammed out monsters act as fodders for extra Deck summon. There are only a few pendulum boss monsters (e.g. Kirin). Even the prominent three pendulum archetypes like Qliphort, Metalfoes and PEPE don't use pendulums as their boss monster. 

Over the years, summoning mechanics have seen enhancements. For example, fusion decks can now fusion summon from Deck, compared to the old school fusions. However, not so much for Pendulums. Pendulum Summon has the least potential to evolve. Their only evolution since their debut is the hybrid pendulum cards. 

Hate for Pendulums

Pendulums receive the most hate from players out of all the mechanics. Now there are several reasons for this.

1. Misconception. Many hate for the mechanic stems from players thinking that the mechanic is overpowered. While it does sound powerful on paper, but in reality, it's a glass cannon. Another misconception is that people think the mechanic requires "no skill," as anyone can add two scales and spam out monsters. However, in reality, adding two random scales into the deck would lead to inconsistency.
2. Recursion and skill gaps. Many players (especially new players) dislike the recursion. Being able to re-summon your destroyed monsters repeatedly sounds problematic until you realize that games in this current meta don't last that long for it to matter. Furthermore, many modern decks have the same recovery ability. However, to a new player, dealing with this recursion can be problematic, which leads to the player feeling cheated. 
3. The first real change. Pendulum summon marks the first time where there was a significant change to the game. They altered the field, and they have a completely different gameplay mechanic.
4. PEPE and QLIPHORT. These two archetypes traumatized many players. These players generally associate ALL pendulum decks as broken like PEPE and Qliphort. Ironic for Qliphort as that deck plays more like a Tribute Summon deck.

Anime Appearance

Despite being the main advertised summoning mechanic during the Arc-V era, pendulum monsters weren't used notably in the Arc-V anime. Out of all the characters, only four of them focused on pendulum monsters (Yuya, Declan, Zarc and Sawatari). The other side characters have a few pendulum monsters that they used once in a while. 

Furthermore, the majority of the time, pendulum summons are used as nothing more than stepping stones for a fusion, synchro or Xyz summon. Some might even argue that Arc-V promoted the other summoning mechanic more.