A copolymer is a chain of repetitive units (monomers) that are almost identical, but they differ in their degree of affinity for certain solvents. A discrete model of such system, based on the simple symmetric random walk, was investigated in [Bolthausen and den Hollander, Ann. Probab. 1997], notably in the weak polymer-solvent coupling limit, where the convergence of the discrete model toward a continuum model, based on Brownian motion, was established. This result is remarkable because it strongly suggests a universal feature of copolymer models. In this talk we show that this is indeed the case. More precisely, we determine the weak coupling limit for a general class of discrete copolymer models based on renewal processes, obtaining as limits a one-parameter family of continuum models, based on stable regenerative sets.