  The collapse of astrophysically significant bodies generates, under suitable
conditions, black holes. Since one expects the generator of the black hole to
be a rotating body, the black hole will also rotate. The existence of inner
singularities in classical solutions for rotating black holes and the fact that
General Relativity is incompatible with Quantum Mechanics lead us to seek for
alternative regular models for rotating black holes. The interest in
singularity-free rotating black holes has grown significantly in recent years,
as shown by the increase in the number of published papers devoted to it.
Undoubtedly, the latest observational developments (LIGO-VIRGO-KAGRA
collaborations, the Event Horizon Telescope or, in the near future, the LISA
project) and the possibility to probe our theoretical predictions have greatly
contributed to awaken the interest.
  This text discusses the general characteristics of regular rotating black
holes. These include the conditions needed to guarantee the absence of
singularities and the consequences that such conditions entail for the
violation of the energy conditions in black hole models. It is argued that
regular rotating black holes do not require an extension through their inner
disk, contrary to classical rotating black holes. In this way, the problems
with negative-mass interpretations and causality violations appearing in
classical solutions could be avoided. It has been included a discussion on the
maximal extension and the usual global causal structure expected for these
spacetimes. The different methods for obtaining regular rotating black holes
are treated, including the use of the generalized Newman-Janis algorithm as an
alibi to derive regular rotating black holes from regular spherically symmetric
static ones. The text also provides an introduction to the thermodynamics and
phenomenology of rotating black holes.
