Cosmological observations indicate that most of the matter in the Universe is Dark Matter. Dark Matter in the form of Weakly Interacting Massive Particles (WIMPs) can be detected directly, via its elastic scattering off target nuclei. Most current direct detection experiments only measure the energy of the recoiling nuclei. However, directional detection experiments are sensitive to the direction of the nuclear recoil as well. Due to the Sun's motion with respect to the Galactic rest frame, the directional recoil rate has a dipole feature, peaking around the direction of the Solar motion. This provides a powerful tool for demonstrating the Galactic origin of nuclear recoils and hence unambiguously detecting Dark Matter. Furthermore, the directional recoil distribution depends on the WIMP mass, scattering cross section and local velocity distribution. Therefore, with a large number of recoil events it will be possible to study the physics of Dark Matter in terms of particle and astrophysical properties. We review the potential of directional detectors for detecting and characterizing WIMPs.