Apparently the matter content of the Universe is dominated by an unknown form of dark matter (DM) without interactions with ordinary baryonic matter, perhaps not even with itself. It only interacts via the gravitational field, manifesting its effects on astrophysical and cosmological scales. The purpose of this review is to summarize the phenomenology of all such effects, that can serve as probes of dark matter. Regardless of the ultimate, correct explanation of its particle nature or field nature, theory needs to address all these effects.
This review does not cover the historical development, except by glimpses, because the rapid development of observational means tends to render all discoveries older than a decade unimportant.
Beginning from the first controversial conclusions from the motion of stars near the Galactic disk on missing matter in the Galactic disk (Sec. 2), and that of Fritz Zwicky in 1933  of missing matter in the Coma cluster (Sec. 3), we describe the kinematics of virially bound systems (Sec. 3) and rotating spiral galaxies (Sec. 4). An increasingly important method to determine the weights of galaxies, clusters and gravitational fields at large, independently of electromagnetic radiation, is lensing, strong as well as weak (Sec. 5). Next follows a discussion of dark matter in elliptical galaxies (Sec. 6) and mass-to-light ratios which probe dark matter in all systems, notably in dwarf spheroidals (Sec. 7). Different ways to measure missing mass in groups and clusters derive from the comparison of visible light and X-rays (Sec. 8). Mass autocorrelation functions relate galaxy masses to dark halo masses (Sec. 9).
In radiation the most important tools are the temperature and polarization anisotropies in the Cosmic Microwave Background (CMB) (Sec. 10), which give information on the mean density of both dark and baryonic matter as well as on the geometry of the Universe. The large scale structures of matter exhibit similar fluctuations evident in the Baryonic Acoustic Oscillations (BAO) (Sec. 11). The amplitude of the temperature variations in the CMB prove, that galaxies could not have formed in a purely baryonic Universe (Sec. 12). Simulations of large scale structures also show that DM must be present (Sec. 13). The best quantitative estimates of the density of DM come from overall parametric fits to cosmological models, notably the Cold Dark Matter model ’ΛCDM’ with a cosmological constant Λ, of CMB data, BAO data, and redshifts of supernovae of type Ia (SNe Ia) (Sec. 14). A particularly impressive testimony comes from merging clusters(Sec. 15). We conclude this review with a brief summary (Sec. 16).