You can see a pretty big list at https://cgit.freedesktop.org/xorg/lib/libX11/plain/nls/en_US.UTF8/Compose.pre.
Math
See the XCOMM Characters from "Mathematical Operators"
section of the compose key list.
Also check out the section on arrows and “XCOMM Latin1 Supplement”.
Sequence  Result  Comment 

8 8  ∞  Infinity 
:   ÷  Division sign 
x x  ×  Multiplication sign 
 _  − 
MINUS SIGN, not to be confused with “” (HYPHENMINUS). 
1 4  ¼  One quarter or “Vulgar fraction one quarter”. 
^ 1  ¹  Superscript 1. 
_ 1  ₁  Subscript 1. 
 >  →  Rightwards arrow 
 ^  ↑  Upwards arrow 
 v  ↓  Downwards arrow. 
= >  ⇒  Rightwards double arrow 
I can’t find ways to enter:

“⋅” (DOT OPERATOR) (It can be entered with US, Symbolic with AltGr+Shift+9)
.  inputs “·” (MIDDLE DOT), which is different.
Misc
Some fractions are just entered with the numerator and denominator.
For example, “¼” is entered using Compose 1 4.
I can’t find a way to easily input a “FRACTION SLASH
” (i.e. “⁄”) though.
Sequence  Result  Comment 

  .  –  En dash 
    —  Em dash 
space space  “ ”  Nobreak space (nonbreaking space). 
" < or < "  “  Left double quote 
" > or > "  ”  Right double quote 
! ?  ‽  Interrobang 
. =  •  Bullet 
Emacs
Emacs has a compose key input method (called “compose
”).
Pretty handy along with activatetransientinputmethod
(Cx \) for entering accents.
Android
For Androidlike operating systems, Unexpected Keyboard (https://github.com/Julow/UnexpectedKeyboard) has a compose key which I really like.
Where are compose sequences defined?
 It seems like it’s in libX11.
 GTK includes its own copy of the X11 Compose file