Recently, an increasing experimental effort has been devoted to the synthesis of complex colloidal particles with chemically or physically patterned surfaces and possible specific shapes that are far from spherical. These new colloidal particles with anisotropic interactions are commonly named patchy particles. In this Perspective article, we focus on patchy systems characterized by spherical neutral particles with patchy surfaces. We summarize most of the patchy particle models that have been developed so far and describe how their basic features are connected to the physical systems they are meant to investigate. Patchy models consider particles as hard or soft spheres carrying a finite and small number of attractive sites arranged in precise geometries on the particle's surface. The anisotropy of the interaction and the limited valence in bonding are the salient features determining the collective behavior of such systems. By tuning the number, the interaction parameters and the local arrangements of the patches, it is possible to investigate a wide range of physical phenomena, from different self-assembly processes of proteins, polymers and patchy colloids to the dynamical arrest of gel-like structures. We also draw attention to charged patchy systems: colloidal patchy particles as well as proteins are likely charged, hence the description of the presence of heterogeneously distributed charges on the particle surface is a promising perspective for future investigations.