The observation of compact binary mergers by the LIGO/Virgocollaboration marked the dawn of a new era in astronomy. LISA willfulfill this vision by opening a new observational window at lowfrequencies. The gravitational radiation emitted by compact binarysystems in these two frequency windows encodes important information ontheir astrophysical formation mechanism. Furthermore, compact objects -whether in isolation or in binaries - are excellent astrophysicallaboratories to probe our understanding of high-energy physics andstrong-field gravity. I will highlight the potential of Earth-and space-based detectors to further our understanding of theformation and evolution of compact binaries. I will also discuss potentialsmoking guns of new physics in gravitational-wave detectors, and thetheoretical and observational challenges associated with their search.
