Abstract：In this talk I will give a general, broad description of the extreme-mass ratioinspiral problem, i.e. the gravitational capture of a stellar-mass compact object via loss of energy due to the emission of gravitational waves. This is one of the most interesting sources of gravitational waves to be detected in the future by a space-borne observatory such as LISA. My talk will mostly be focused on astrophysics but will include bits of general relativity as well. Time allowing, I will present a new source of gravitational waves, the so-called extremely-large mass ratio inspirals.