As we touched on previously, the first Puyo Puyo game was released in 1991, the brainchild of designer Moo Niitani (real name Masamitsu Niitani). The first home releases were very simple, with only single player modes where you can either make chains endlessly for highscores or the "Mission" mode where you have to clear preset boards with certain numbers of Puyo.
Puyo really became what we know it as today with the arcade release a year later, also called Puyo Puyo, but with a competitive multiplayer mode added. It also added a story mode, populated with Madou Monogatari characters. While the MM games have some sort of semblance to a coherent plot and believability, the Puyo games have taken the characters and even minor villains from the games and turn them into hilarious caricatures. Some of the characters you will find include:
There are also many more characters but these are the main ones, most of whom recur throughout the whole series, even in the newer games where most of the original cast has been discarded.
The mechanics of the game is exactly as described in the introduction. You make chains and drop garbage on the opponent field. This is the competitive Puyo at its simplest form. In single-player battles, each CPU will even have their own strategy for playing, such as Suketoudara firing quick 2-3 chains at you, Harpy stacking Puyo on the left and rightmost columns to try to make "luck" chains and Skeleton-T's strategy seems to involve him mashing his face into the controller. It is a nice touch and indeed many human players will utilize similar strategies to these CPU players.
A notable fact about this game is that it spawned quite a few official clones that were distributed in the West, and since the original was never released on consoles in English, these clone versions were the games that introduced many Western players to the series. Puyo Puyo was licensed to Sega who replaced the cast with Sonic characters and called it Dr. Robotnik's Mean Bean Machine and to Nintendo who did the same with Kirby characters and renamed it Kirby's Avalanche (Kirby's Ghost Trap in Europe). There are also various other lesser-known clones, such as a Lion King-themed one called Timon and Pumbaa's Bug Drop and Qwirks, a generic clone marketed with the name of creator of Tetris, Alexey Pajitnov, despite him not being involved in any way with the game.
For those of you who feel like going through the story mode with hilarious pseudo-English translation, an English version of the arcade release can be found by looking for the ROM called "Puyo Puyo (World)".