The concepts of functional precision polymers and the latest accomplishments in their synthesis are summarized. Synthetic concepts based on chain growth polymerization are compared to iterative synthetic approaches. Here, the term "functional precision polymers" refers to polymers that are not solely hydrocarbon-based but contain functional groups and are characterized by a highly ordered primary structure. If insertion polymerization is used for their synthesis, olefin metathesis-based polymerization techniques, that is, ring-opening metathesis polymerization (ROMP), acyclic diene metathesis (ADMET) polymerization, and the regio- and stereoselective cyclopolymerization of α,ω-diynes are almost exclusively applied. Particularly with regio- and stereospecific ROMP and with cyclopolymerization, the synthesis of tactic polymers and copolymers with high regio-, stereo-, and sequence control can be accomplished; however, it requires carefully tailored transition metal catalysts. The fundamental synthetic concepts and strategies are outlined.