In complex systems, external parameters often determine the phase in which the system operates, i.e., its macroscopic behavior. For nearly a century, statistical physics has extensively studied systems' transitions across phases, (universal) critical exponents, and related dynamical properties. In this talk I will consider the functionality of systems, notably operations in socio-technical ones, production in economic ones and possibly information-processing in biological ones, where timing is of crucial importance. I will introduce a stylised model on temporal networks with the magnitude of delay-mitigating buffers as the control parameter. I will show that the model exhibits temporal criticality, a novel form of critical behavior in time. I will characterize fluctuations near criticality, commonly referred to as "avalanches'', and identify the corresponding critical exponents. I will also show that real-world temporal networks, too, exhibit temporal criticality.