Compact object binaries are known to be factories of rich information and prime targets in GW astronomy. Their formation, evolution, and final phase provoke many questions, and with the enhanced strength of GW detectors, many of these questions are slowly getting answered! In this talk, we will discuss these binaries buried in different astrophysically motivated environments. In particular, we will be discussing the detection and modeling aspects of these binaries and probing the environments in which these binaries evolve. To a large extent, we will consider binaries with extreme or intermediate mass ratios, which are the key sources for space-based detectors like LISA. We will discuss how these environmental effects find their way into binary evolution and waveform modeling, and more importantly, how resonances can be a useful tool to understand these effects.