In these lectures, I describe a variety of efforts to identify or constrain the identity of dark matter by detecting the annihilation or decay products of these particles, or their effects. After reviewing the motivation for indirect searches, I discuss what we have learned about dark matter from observations of gamma rays, cosmic rays and neutrinos, as well as the cosmic microwave background. Measurements such as these have been used to significantly constrain a wide range of thermal relic dark matter candidates, in particular those with masses below a few hundred GeV. I also discuss a number of anomalies and excesses that have been interpreted as possible signals of dark matter, including the Galactic Center gamma-ray excess, the cosmic-ray antiproton excess, the cosmic-ray positron excess, and the 3.5 keV line. These lectures were originally presented as part of the 2018 Theoretical Advanced Study Institute (TASI) summer school on ``Theory in an Era of Data''. Although intended for advanced graduate students, these lectures may be useful for a wide range of physicists, astrophysicists and astronomers who wish to get an overview of the current state of indirect searches for dark matter.