Periodically driven quantum systems exhibit a larger spectrum of properties than their continuos equivalents and have the advantage that they are easier to simulate by available quantum hardware. In this talk I will discuss a few examples of quantum Floquet evolutions that are possible to simulate on the quantum hardware. I will start with the discussion of the simplest system, 1D chain of spins subject to XY or XYZ evolution and show that they display roughly the same properties as their continuous analogues. This simple system provides the best test platform for the quantum hardware simulations and some of the theoretical predictions have been already confirmed experimentally. I will also argue that it is much easier to produce topologically non-trivial states for a periodically driven systems than for continous ones and give some examples where one expects such states to appear for the dynamics that becomes completely trivial in the continous limit.