LISA, the Laser Interferometer Space Antenna, is a joint mission between the European Space Agency and the National Aeronautics and Space Administration (USA) scheduled to fly in about 10 years. Its primary scientific goal is to carry out low-frequency gravitational wave astronomy, opening in this way a completely new window to the exploration of the universe that is expected to lead to dramatic discoveries in astrophysics and cosmology, as well as tests of the validity of general relativity. The main aim of this proposal is to contribute to the development of LISA science by focusing on the study of one of the main LISA targets: The inspiral, driven by gravitational radiation emission, of compact objects into supermassive black holes sitting at the galactic centers. Of particular relevance are the so-called extreme-mass-ratio inspirals (EMRIs). The main goals of the research planned in this proposal are: (i) Simulations of EMRIs and other Inspirals: In order to extract the signals produced by these systems, which will be buried in instrumental noise and the gravitational wave foreground, and later extract relevant physical information from them, we need to have an a priori theoretical knowledge of the gravitational waveforms with a certain degree of precision. This knowledge can be obtained from simulations of these inspirals using perturbative general relativity. (ii) LISA phenomenology: To explore possible astrophysical scenarios that can lead to inspirals inside the LISA band, and to investigate the type and quality of the information that could be extracted from different inspiral mechanisms.