The Mantis and Crane styles are a form of assassination arts used by Gen in the Street Fighter series. They are specifically and respectively referred to in the games' storyline as the Assassination Fist: Mourning Style (暗殺拳・喪流, Ansatsuken Sō Ryū) and the Assassination Fist: Memorial Style (暗殺拳・忌流, Ansatsuken Ki Ryū).
The two styles are actually an amalgamation of various Chinese kung-fu styles that Gen trained in during his years as an assassin.
Gen's Sou-style special moves include the Hyaku-Ren-Kou (百連勾 Hyakurenkō?, "Hundred Chained Hooks") and the Geki-Rou (逆瀧 Gekirō?, "Inverted Cascade"). His Super Combos include the Zan-ei (惨影? the "Cruel Shadow") and the Shitenshu (死点咒 Shitenshū?, "Death Point Curse").
Gen's Ki-style special moves includes the Jyasen (蛇穿 Jasen?, "Snake Drill"), and the Ouga (徨牙 Ōga?, "Wandering Fang"). His Super Combos include the Jya-Kou-Ha (蛇咬叭 Jakōha?, "Snake Bite Opening") and the Kouga (狂牙 Kōga?, "Lunatic Fang").
In the games, Gen is able to switch between the two styles at any time by pressing all three punch or kick buttons, respectively; the move can be used in the middle of most attacks.
When Gen is played on X-ism mode in Street Fighter Alpha 3, he loses the ability to switch between fighting styles. Instead, he has a blended style which uses techniques from both styles (except the Oga), and uses the Zan'ei as his sole Super Combo.
In the Street Fighter IV series, Gen is the only character to have two Super Combos and four Ultra Combos (one Super and two Ultras for each style) as a result of this mechanic. His Ultra Combos are the Zetsuei and Ryukoha (I), and the Shitenketsu and Teiga (II).
The Mantis style is a defense-oriented style that is the 'easier' to use of the two. Gen's Mantis moves contain a few solid tools for poking at and pressuring foes, and its techniques are mainly ground-based. Gen is one of only two characters to retain the Alpha series' Chain Combo ability from Street Fighter Alpha 2 (the other being Guy), which can be used in this style.
Conversely, the Crane style is designed to be offensive, attacking the foe from various (and mostly air-based) angles. Gen's jump arc becomes wider, and many of his moves gain an altered 'trajectory', e.g. standard normals that can hit overhead and low. In Crane style, Gen can easily punish attacks and create confusing cross-ups, though this leaves him more open to attacks.
Many of Gen's best combos in his appearances require at least one switch between styles mid-attack, usually from Mantis into Crane.