Recent theoretical and experimental progress on synthetic quantum systems, such as cold atoms in optical lattices, trapped ions, and solid-state devices subject to periodic potentials in space and time, has ushered in a new era of engineered quantum dynamics in and out of equilibrium. A central theme of this progress is the exquisite in-situ control allowing the realization and the probing of novel quantum phases of matter. In this context, I will present our recent and ongoing theoretical work on engineering nontrivial electronic bands by coherent spatiotemporal modulations. This includes, in particular, engineering novel phases and functions of graphene structures irradiated by light, and a new type of magic-angle phenomenon realized in twisted heterostructures of AA-stacked graphene bilayer with other graphene multilayers with band touching, which we dub "Dirac magic".
