Anomalous transport effects arise from the interplay of quantum anomalies with electromagnetic fields and vorticities, constituting one of the most fascinating manifestations of the topological nature of the QCD vacuum. In this talk, I will present a lattice QCD study of two of the most prominent examples of these phenomena, the Chiral Magnetic Effect (CME) and the Chiral Separation Effect (CSE). In the case of the CSE, I will discuss the first determination in physical QCD of the in-equilibrium conductivity of an anomalous transport effect, showing that is greatly affected by temperature and chiral symmetry restoration. For the CME, I will present in detail why this effect is absent in global equilibrium, as well as how it is modified in the presence of inhomogeneous magnetic fields, which resemble the physical situation in heavy-ion collision experiments. Finally, I will show preliminary results for the the out-of-equilibrium CME conductivity, which can be calculated on the lattice via spectral reconstruction methods.