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If the spectral gap above the ground state(s) of a family of quantum lattice models with short-range interactions depending on a continuous parameter lambda, has a positive lower bound independent of lambda and the size of the system, we say that the ground states belong to the same gapped quantum phase. We present new results characterizing gapped quantum phases. In particular, we discuss the role of edge excitations, the "protection" effect of an unbroken local symmetry, and the particle nature of elementary excitations. This talk is based on joint work with Sven Bachmann, Jutho Haegeman, Eman Hamza, Spirydon Michalakis, Tobias Osborne, Norbert Schuch, Robert Sims, Frank Verstraete, and Amanda Young.