Gravitational wave (GW) astronomy demands an enormous amount of waveform templates, both to search for new GW events and to properly infer the parameters of the GW sources, primarily compact binary coalescences (CBCs). In this talk I will review the essential points of the effective one-body (EOB) approach, which currently stands as the most complete, robust and predictive analytical framework to build templates for GW signals produced by CBCs. I will then discuss the role, in this modeling procedure, of the binary orbital eccentricity, whose inclusion in GW models has attracted a growing interest in the last few years. In this context, I will present the outcomes of several works we carried out with the aim of including eccentricity effects in the EOB-based model TEOBResumS, while preserving the factorized and resummed waveform structure which this model entails.