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In topological quantum computing quantum information is stored in certain topologically-ordered states of matter and quantum computation will be carried out by braiding the world-lines of quasiparticle excitations that obey non-Abelian statistics in specific patterns. Since the storage and manipulation of quantum information depends only on the global properties of the system this method of quantum computing is (in principle) intrinsically fault tolerant. I will review the basic properties of topological states and briefly describe a general method for finding braiding patterns that correspond to a universal set of quantum gates on encoded topological qubits, based on quasiparticles that can be realized as excitations of certain fractional quantum Hall states.