Recent progress observed in Topological Polymer Chemistry is outlined with particular emphasis on single-cyclic (ring) and multi-cyclic polymers having programmed chemical structures, now becoming obtainable with guaranteed purity by newly developed synthetic protocols. By making use of these topological polymers, unprecedented opportunities have now been realized to provide new insights on fundamental polymer properties either in solution or bulk, in static or dynamic states, or in selfassemblies. Moreover, unusual properties and functions for polymer materials have now been revealed based on their cyclic topologies, i.e., topology effects, unattainable either by linear or branched counterparts.