Over the past few decades, a consensus picture has emerged in which roughly a quarter of the universe consists of dark matter. I begin with a review of the observational evidence for the existence of dark matter: rotation curves of galaxies, gravitational lensing measurements, hot gas in clusters, galaxy formation, primordial nucleosynthesis and Cosmic Microwave Background (CMB) observations. Then, I discuss a number of anomalous signals in a variety of data sets that may point to discovery, though all of them are controversial. The annual modulation in the DAMA detector and/or the gamma-ray excess seen in the Fermi Gamma Ray Space Telescope from the Galactic Center could be due to WIMPs; a 3.5 keV X-ray line from multiple sources could be due to sterile neutrinos; or the 511 keV line in INTEGRAL data could be due to MeV dark matter. All of these would require further confirmation in other experiments or data sets to be proven correct. In addition, a new line of research on dark stars is presented, which suggests that the first stars to exist in the universe were powered by dark matter heating rather than by fusion: the observational possibility of discovering dark matter in this way is discussed.