A many-body system to periodic driving often exhibits primarily destructive effects such as heating. Remarkable new research has however shown that such periodic driving can lead to new routes to "quantum control". For instance, a well-tailored driving protocol can be used to enhance or induce desired collective properties. As a toy model we will discuss dynamical control of a parametric oscillator, where the oscillator frequency can be stabilized via high-frequency driving. We then discuss a novel phenomenon in solid state physics termed light-enhanced superconductivity, which is visible in the conductivity, which has been experimentally observed to be stabilized by THz radiation. We discuss our proposed mechanism for this effect which is based on parametric amplification. As an example for a driven system in which the emergent state is qualitatively distinct from the non-driven case, we will discuss periodic driving of an ultracold atom system in a triangular lattice. Here, the periodic driving results in a synthetic gauge field which gives rise to a chiral superfluid state.