Deformed relativistic symmetry principles

We review the main features of models where relativistic symmetries are deformed at the Planck scale. We cover the motivations and links to other quantum gravity approaches. We describe in some detail the most studied theoretical frameworks, including Hopf algebras, relative locality, and other scenarios with deformed momentum space geometry. We discuss possible phenomenological consequences, and point out current open questions.Comment: Invited contribution as a chapter to the book "Modified and Quantum Gravity - From theory to experimental searches on all scales" (C. L\"ammerzahl and C. Pfeifer (eds.), Springer