  The development of electron spin resonance (ESR) combined with scanning
tunneling spectroscopy (STM) is undoubtedly one of the main experimental
breakthroughs in surface science of the last decade thanks to joining the
extraordinarily high energy resolution of ESR (nano-eV scale) with the
single-atom spatial resolution of STM (sub-\AA ngstr\"om scale). While the
experimental results have \fer{significantly} grown with the number of groups
that have succeeded in implementing the technique, the physical mechanism
behind it is still unclear, with several different mechanisms proposed to
explain it. Here, we start by revising the main characteristics of the
experimental setups and observed features. Then, we review the main theoretical
proposals, with both their strengths and weaknesses. One of our conclusions is
that many of the proposed mechanisms share the same basic principles, \fer{the
time-dependent electric field at the STM junction is modulating the coupling of
the spin-polarized transport electrons with the local spin.} This explains why
these mechanims are
  essentially equivalent in a broad picture. We analyze the subtle differences
between some of them and how they compare with the different experimental
observations.
