  Since Albert Einstein's seminal 1905-paper on Brownian motion, the
temperature of fluids and gases of known viscosity can be deduced from
observations of the fluctuations of small suspended probe particles. We
summarize recent generalizations of this standard technique of Brownian
thermometry to situations involving spatially heterogeneous temperature fields
and other non-equilibrium conditions in the solvent medium. The notion of
effective temperatures is reviewed and its scope critically assessed. Our
emphasis is on practically relevant real-world applications, for which
effective temperatures have been explicitly computed and experimentally
confirmed. We also elucidate the relation to the more general concept of
(effective) temperature spectra and their measurement by Brownian
thermospectrometry. Finally, we highlight the conceptual importance of
non-equilibrium thermometry for active and biological matter, such as
microswimmer suspensions or biological cells, which often play the role of
non-thermal ('active') heat baths for embedded Brownian degrees of freedom.
