The last decade has witnessed a renewed interest in the coarse-grained (CG) models for biopolymers, also stimulated by the needs of modern molecular biology, dealing with nano- to micro-sized bio-molecular systems and larger than microsecond timescale. This combination of size and timescale is, in fact, hard to access by atomic-based simulations. Coarse graining the system is a route to be followed to overcome these limits, but the ways of practically implementing it are many and different, making the landscape of CG models very vast and complex. In this paper, the CG models are reviewed and their features, applications and performances compared. This analysis, restricted to proteins, focuses on the minimalist models, namely those reducing at minimum the number of degrees of freedom without losing the possibility of explicitly describing the secondary structures. This class includes models using a single or a few interacting centers (beads) for each amino acid. From this analysis several issues emerge. The difficulty in building these models resides in the need for combining transferability/predictive power with the capability of accurately reproducing the structures. It is shown that these aspects could be optimized by accurately choosing the force field (FF) terms and functional forms, and combining different parameterization procedures. In addition, in spite of the variety of the minimalist models, regularities can be found in the parameters values and in FF terms. These are outlined and schematically presented with the aid of a generic phase diagram of the polypeptide in the parameter space and, hopefully, could serve as guidelines for the development of minimalist models incorporating the maximum possible level of predictive power and structural accuracy.