The synthesis of polyionic polymers can be categorized into two main methods: polymerization of monomers containing ionic groups and post-polymerization modification of neutral polymers to introduce ionic groups. Techniques like free-radical polymerization, atom transfer radical polymerization (ATRP), and reversible addition-fragmentation chain transfer (RAFT) are commonly used for their synthesis. The choice of method depends on the desired properties and applications of the final product.