There is an ever-increasing demand for higher-performing polymeric materials counterbalanced by the need for sustainability throughout the life cycle. Copolymers comprising ester, carbonate, or ether linkages could fulfill some of this demand as their monomer-polymer chemistry is closer to equilibrium, facilitating (bio)degradation and recycling; many monomers are or could be sourced from renewables or waste. Here, an efficient and broadly applicable route to make such copolymers is discussed, a form of switchable polymerization catalysis which exploits a single catalyst, switched between different catalytic cycles, to prepare block sequence selective copolymers from monomer mixtures. This perspective presents the principles of this catalysis, catalyst design criteria, the selectivity and structural copolymer characterization tools, and the properties of the resulting copolymers. Uses as thermoplastic elastomers, toughened plastics, adhesives, and self-assembled nanostructures, and for programmed degradation, among others, are discussed. The state-of-the-art research into both catalysis and products, as well as future challenges and directions, are presented.