The topological properties, both in and out of equilibrium, of strongly interacting matter described by Quantum Chromodynamics is a subject of intense research in the recent years. In this talk I will discuss some of our very recent results in this area through the application of newly developed lattice gauge theory techniques. Firstly I will discuss our latest results on the topological susceptibility of QCD for a wide range of temperatures, and explain how it allows us to understand the microscopic topological properties of QCD. Using these results we are now able to set bounds on the axion mass if indeed axions are cold dark matter candidates, which can be tested in the ADMX experiment. In the context of non-equilibrium QCD I will discuss the recent progress we made in understanding the anomalous dynamics of fermions in presence of topological transitions and magnetic fields using lattice techniques. I will also briefly discuss the possible applications of our real-time techniques in strongly correlated systems beyond QCD.