In this talk, I will discuss energy dissipation and heating in slowly driven quantum systems, focusing on topological driving schemes. In the first part of my talk, I will present a system in which many-body dynamics lead to the emergence of a quasi-steady state with a high entropy density and yet robust topological transport. I will explain the mechanisms behind this phenomenon and demonstrate the emergence of the quasi-steady state on an exactly solvable strongly coupled fermionic model. In the second part of my talk, I will show that the dissipation of energy in nearly adiabatic quantum systems is linked to the quantum geometry of the problem. Interestingly, this result implies a topological bound on the energy dissipation rate in a class of topological systems. Our findings uncover new connections between topology and dissipation in slowly driven quantum systems, shedding light on their fundamental properties and potential for practical applications, such as the development of optimized driving protocols for topological drives.