One of the major challenges of modern physics is to decipher the nature of dark matter. Astrophysical observations provide ample evidence for the existence of an invisible and dominant mass component in the observable universe. The dark matter could be made of new, yet undiscovered elementary particles, with allowed masses and interaction strengths with normal matter spanning an enormous range. Among these, particles with masses in the MeV-TeV range could be directly observed via elastic or inelastic scatters with atomic nuclei or with electrons in ultra-low background detectors operated deep underground. After an introduction to the dark matter problem and the phenomenology of direct dark matter detection, I will discuss the most promising direct detection techniques, addressing their current and future science reach, as well as their complementarity.