Quantum coherence plays essential role in diverse phenomena of relevance in the early universe. Examples include activation of sterile neutrinos, electroweak baryogenesis, resonant leptogenesis and particle production in phase transitions and during the (p)reheating stage after inflation. After a general introduction I will concentrate on the particle production problem. I will show how one can derive coupled, renormalized and tractable quantum kinetic equations for the scalar field 1- and 2-point functions starting from the CTP-formalism, working in the Hartree approximation of the 2PI-action. I will then apply these equations to study particle production and the back-reaction from the non-equilibrium modes on the dynamics of the one-point function. We will see both spinodal and parametric resonances taking place and sometimes overlapping in a novel way, and we follow the process of decoherence and thermalization. Overall, I argue that advanced quantum transport equations are necessary for an accuarate description of many systems of acute interest in cosmology.