I will talk about the advances in the field of quantum simulation, discuss possible strategies, and present recent results on quantum simulation with the Floquet approach. Searching for optimal algorithms for the modern setups with limited resources, I will show that it can be used as an efficient quantum simulation strategy for superconducting circuits platform. Considering the example of a modern transmon-based sample, this for instance can allow to simulate various spin models using periodically modulated drives. Next, I will discuss its potential application for the observation of discrete time crystals. Finally, the roadmap for studying symmetry protected topological phases with superconducting circuits will be presented.