Measurement is an intrinsically non-unitary quantum process. It enables rich physics beyond equilibrium and unitary quantum dynamics. In particular, novel critical behavior in quantum dynamical systems subject to measurements has recently attracted tremendous attention. Despite abundant numerical evidence of such novel quantum criticality, theoretical understanding of the underlying universality classes is quite limited for general dynamical systems. In this talk, I will present a theoretical framework for studying the universal behavior of general dynamical non-interacting fermion systems whose dynamics is driven by both unitary evolution and measurements. The framework is based on a general correspondence between these dynamical non-interacting fermion systems and the classic disordered fermion systems encountered in Anderson localization problems. I will show that, under this framework, the dynamical non-interacting fermion systems are classified according to their symmetry and topology. Also, I will discuss how to use this framework to capture the measurement-induced quantum critical behavior in dynamical non-interacting fermion systems. In particular, I will show that, depending on the measurement protocol, the dynamical fermion systems can exhibit quantum criticality that shares the same universality classes as Anderson localization transitions and novel universality classes beyond Anderson localization.