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Driven quantum systems can lead to novel and interesting phases of matter. In this talk, we will summarize recent results on phase structures and phase transitions in the context of driven Conformal Field Theories in two dimensions and beyond. In particular, we will discuss how non-trivial (dynamical, non-equilibrium) phases emerge that can be classified according to the conjugacy classes of the corresponding sl(2,R) transformation. We will also explain how a geometric (more generally, Holographic) (quantum) gravitational dual description encodes the information of these phases and how the experience of a bulk observer is encoded in the CFT Hamiltonian. Finally, we will conclude with potential future directions.