Textbook quantum criticality refers to phenomena which originate in states which scale-invariant in both space and time, occurring at continuous  zero-temperature phase transitions. Various experimental findings have raised interest in local forms of quantum criticality, where scale invariance in space in either absent or irrelevant. Prominent examples include variants of the Mott metal-to-insulator transition in a number of strongly correlated electron compounds. After an extended introduction, I will discuss one of the simplest cases, namely the bandwidth-tuned Mott transition in a single-band setting. Recent transport studies, both theoretical and experimental, near this transition have uncovered –surprisingly – apparent quantum critical scaling of the electrical resistivity at elevated temperatures, despite the fact that the actual low-temperature phase transition is of first order. This raises the question whether there is a hidden Mott quantum critical point. I will argue that the dynamical mean-field theory of the Hubbard model admits, in the low-temperature limit, scale-invariant (i.e. power-law) solutions which had been overlooked before. It is this incoherent power-law regime, corresponding to approximate local quantum criticality, which is continuously connected to and responsible for the apparent quantum critical scaling above the classical critical end point. I will discuss the role of magnetic frustration in these phenomena, non-local corrections, and broader implications for the phenomenology of bad metals.