Explore the fascinating world of exotic compact objects and their gravitational-wave signatures in this comprehensive lecture by Andrea Maselli from the International Centre for Theoretical Sciences. Delve into the history of black holes, their experimental observations, and their presence in the cosmos. Examine the motivations for seeking alternatives to black holes and discover the formation, evolution, and characteristics of exotic compact objects (ECOs). Compare ECOs with black holes and learn where to search for these intriguing celestial bodies. The lecture also covers effective potentials and provides valuable references for further study. Gain insights into cutting-edge research in gravitational-wave astronomy and expand your understanding of theoretical physics and astrophysics.