  The inspirals of stellar-mass mass compact objects into massive black holes
in the centres of galaxies are one of the most important sources of
gravitational radiation for space-based detectors like LISA or eLISA. These
extreme-mass-ratio inspirals (EMRIs) will enable an ambitious research program
with implications for astrophysics, cosmology, and fundamental physics. This
article is a summary of the talks delivered at the plenary session on EMRIs at
the 10th International LISA Symposium. It contains research updates on the
following topics: astrophysics of EMRIs; EMRI science potential; and EMRI
modeling.
