Coacervates are condensed liquid-like droplets formed by liquid-liquid phase separation of molecules through multiple weak associative interactions. In recent years it has emerged that not only long polymers, but also short peptides are capable of forming simple and complex coacervates. The coacervate droplets they form act as compartments that sequester and concentrate a wide range of solutes, and their spontaneous formation make coacervates attractive protocell models. The main advantage of peptides as building blocks lies in the functional diversity of the amino acid residues, which allows for tailoring of the peptide's phase separation propensity, their selectivity in guest molecule uptake and the physicochemical and catalytic properties of the compartments. The aim of this tutorial review is to illustrate the recent developments in the field of peptide-based coacervates in a systematic way and to deduce the basic requirements for both simple and complex coacervation of peptides. We review a selection of peptide coacervates that illustrates the essentials of phase separation, the limitations, and the properties that make peptide coacervates biomimetic protocells. Finally, we provide some perspectives of this novel research field in the direction of active droplets, moving away from thermodynamic equilibrium.