In How are dances written down and passed along? Cecil talked about Labanotation. This is used for ballet, modern, and other dance forms, and is so complicated because it tries to cover every possiblity and body position.
There are other notations that are much easier to read because they assume that there is a common basis that people already know, and they generally cover one specific dance style. I have at home many folders full of choreographed dances in ballroom (waltz, foxtrot, quickstep, rhumba, cha, jive, etc); percussive dance (tap, clogging, irish hardshoe); street latin (salsa, rueda, samba de gafiera, forro, zouk, bolero etc). Mostly I dance freestyle, but with a bit of practice I could soon dance any one of the dances on those sheets, even if I didn’t learn or see it before. The style may be different, but not much.