Hot microswimmers are self-propelled Brownian particles that exploit local heating for their directed self-thermophoretic motion. We provide a pedagogical overview of the key physical mechanisms underlying this promising new technology. It covers the hydrodynamics of swimming, thermophoresis and -osmosis, hot Brownian motion, force-free steering, and dedicated experimental and simulation tools to analyze hot Brownian swimmers. a arXiv:1805.07150v1 [cond-mat.soft] 18 May 2018 with self-thermophoresis than with conventional macroscopic thermophoresis. Selfthermophoresis is thus arguably an interesting and technologically promising propulsion mechanism, with some important advantages over other designs. i) Universality, Availability, Biocompatibility: it does not rely on exotic (maybe poisonous) solvents or fuels, but exploits a comparatively "universal" mechanism. It does not run out of fuel and is minimally invasive, since the heating is local and sizable motion can already be achieved with minor heating of the surroundings. ii) Control: the propulsion speed can be regulated continuously and propulsion can instantly be switched on and off, e.g. by using conventional lasers and microscopy equipment. Thanks to emerging efficient cooling mechanisms for colloidal particles [4], one can even imagine fabricating particles with a reverse gear. Besides, efficient force-free steering mechanisms such as photon nudging [5] are already available. iii) Versatility: heating can be realized by a variety of methods, such as the absorption of laser light by metal or carbon parts, or of microwaves by super-paramagnetic parts, which opens up the possibility of combining several independent and independently addressable thermophoretic propulsion mechanisms into one microstructure. A whole community of researchers is moreover interested in micro-and nano-particle heating for its own sake [6]. iv) Scalability: downscaling does not reduce the propulsion speed [5] but increases the efficiency [7]. Synthesis, speed control, and steering [5] of self-thermophoretic swimmers, as well as their photothermal detection [8], are all scalable to nanoscopic dimensions. The remainder of the paper is structured as follows. The next section reviews the distinction between self-phoretic, phoretic, and passive motion and the concomitant flow fields excited in the solvent, on a hydrodynamic level. This means that the physical mechanism that actually drives the motion is confined to such a narrow boundary layer that it is sufficiently well captured by a mere hydrodynamic boundary condition for the solvent flow. On this level, the theory of swimming is universal and independent of the actual propulsion mechanism. The following section provides a closer look at the engine of the swimmer, namely the processes of phoresis and self-phoresis of heated particles. The basic principles of self-thermophoretic propulsion and the underlying osmotic processes are very similar to those in other phoretic phenomena, such as diffusiophoresis and electrophoresis. In fact, ...