Protein structures are classically described as composed of two regular states, the α-helices and the β-strands and one non-regular and variable state, the coil. Nonetheless, this simple definition of secondary structures hides numerous limitations. In fact, the rules for secondary structure assignment are complex. Thus, numerous assignment methods based on different criteria have emerged leading to heterogeneous and diverging results. In the same way, 3 states may over-simplify the description of protein structure; 50% of all residues, i.e., the coil, are not genuinely described even when it encompass precise local protein structures.Description of local protein structures have hence focused on the elaboration of complete sets of small prototypes or "structural alphabets", able to analyze local protein structures and to approximate every part of the protein backbone. They have also been used to predict the protein backbone conformation and in ab initio / de novo methods. In this paper, we review different approaches towards the description of local structures, mainly through their description in terms of secondary structures and in terms of structural alphabets. We provide some insights into their potential applications.