Abstract. Chemically active colloids locally change the chemical composition of their solvent via catalytic reactions which occur on parts of their surface. They achieve motility by converting the released chemical free energy into mechanical work through various mechanisms, such as phoresis. Here we discuss the theoretical aspects of self-diffusiophoresis, which -despite being one of the simplest motility mechanisms -captures many of the general features characterizing self-phoresis, such as self-generated and maintained hydrodynamic flows "driven" by surface activity induced inhomogeneities in solution. By studying simple examples, which provide physical insight, we highlight the complex phenomenology which can emerge from self-diffusiophoresis.