ABSTRACT: Quantum information theory has promoted the distinct features of quantum mechanics - such as superposition, the uncertainty principle, and quantum correlation and entanglement - from philosophical curiosities to practical resources for quantum information-processing protocols with promising advantages over their classical counterparts. On the other hand, since the early days, there have been significant efforts to better understand the perplexing quantum statistics as some sort of modification of classical statistics. A powerful tool in this direction is quasiprobability, a quantum analogue of classical phase-space distributions that can have nonpositive (i.e., negative and/or nonreal) values. A natural question arises whether these anomalous values of quasiprobability can be used to quantify the amount of resourcefulness of a quantum system. In my talk, I will discuss our recent attempts to use the nonpositive values of the Kirkwood-Dirac quasiprobability, and also a related concept of strange nonreal weak value, to characterize and quantify quantum coherence, asymmetry, genuine quantum uncertainty, bipartite nonclassical correlation and entanglement, and a notion of quantum speed limit of observable.