  We introduce a general method for the construction of quasiprobability
representations for arbitrary notions of quantum coherence. Our technique
yields a nonnegative probability distribution for the decomposition of any
classical state. Conversely, quantum phenomena are certified in terms of signed
distributions, i.e., quasiprobabilities, and a residual component unaccessible
via classical states. Our unifying method combines well-established concepts,
such as phase-space distributions in quantum optics, with resources of
quantumness relevant for quantum technologies. We apply our approach to analyze
various forms of quantum coherence in different physical systems. Moreover, our
framework renders it possible to uncover complex quantum correlations between
systems, for example, via quasiprobability representations of multipartite
entanglement.
