Abstract: Artificial micro-swimmers are vital in the study of biological systems and non-equilibrium phenomena. A prime example is given by autophoretic particles, such as Janus particles, which self-propel due to asymmetric chemical interactions on their surface. The chemical gradients generated by the particle induce an osmotic pressure, which is balanced by viscous stresses driving an effective slip flow confined to a thin layer at the surface of the particle. The particle thus sets the surrounding fluid in motion, which then reacts back on the particle, creating surface stresses and eventually self-propulsion. Here, we develop an analytical and numerics-friendly formalism to study autophoresis based on general principles such as linearity of the governing equations. Choosing a kinetic approach, thermal fluctuations of the suspending fluid are included systematically. After discussing the central ideas of our method, we study the concrete example of a bottom-heavy Brownian Janus particle in confinement. Finally, we give an outlook on potential future applications.