An increasing theoretical and experimental effort has been recently dedicated to the design and the fabrication of colloidal particles that may recognize each other and organize themselves via directional and specific interactions. These new colloidal particles exhibit a site-specific engineering of their surface and are commonly named patchy particles. In this article, we review the theoretical studies that describe the self-assembly of patchy colloids with an increasing number of patches and make the link with the experimental studies that have already allowed or might be used for the synthesis of the corresponding colloids.