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The nature of dark matter remains one of the biggest mysteries in cosmology. Among the many possible candidates, one of the most well-motivated class of models and leading candidate is the ultra-light dark matter. This class represents the lightest possible dark matter candidates and exhibits a wave-like behavior on galactic scales. This leads to a rich phenomenology on small scales that can potentially not only reconcile the CDM picture with the small-scale behavior of dark matter but offer us the unique possibility to probe their distinctive predictions and imprints that can reveal clues about the internal properties of dark matter. In this colloquium, I will review this class of models, describing and classifying the different constructions and their phenomenology. Given their vast cosmological and astrophysical effects on observables, I will describe the ongoing advances in constraining these models using current gravitational tests, and highlight the strong constraining power of small-scale astrophysical observations. Current and future observations of these systems present a powerful and, still not fully explored, gravitational laboratory that can reveal the fundamental physics of dark matter in the next few years.