There are a few major types of polymers used and then there are some minor ones used as well.
Polyamines – nonionic bridge particles together. Anionic and cationic formed by copolymerizing with acrylic acid or cationic monomer.
Poly (Diallyl Dimethyl Ammonium Chloride) – similar to polyamines but can be copolymerized with other monomers.
Polyacrylamides – usable in various pHs
Polysaccharides – guar gums, used in acid