String-net condensation is a physical mechanism for topological phases. Quantum systems of extended objects naturally give rise to a large class of exotic phases, namely topological phases, when these objects become highly fluctuating and condense. The authors derive exactly soluble Hamiltonians for 2D local bosonic models whose ground states are string-net condensed states. These ground states correspond to 2D parity invariant topological phases. The models reveal the mathematical framework underlying topological phases: tensor category theory. One of the Hamiltonians, a spin-1/2 system on the honeycomb lattice, is a simple theoretical realization of a fault tolerant quantum computer. In 3D, string-net condensation naturally gives rise to both emergent gauge bosons and fermions, unifying them in 3 and higher dimensions. The paper introduces the string-net picture in the context of gauge theory, showing that all deconfined gauge theories can be understood as string-net condensates. The authors argue that all doubled topological phases are described by string-net condensation. They construct fixed-point wave functions for each string-net condensed phase, which are associated with a six-index object satisfying certain algebraic equations. These wave functions capture the universal properties of the corresponding phases. The authors also construct fixed-point Hamiltonians for these phases, which are exactly soluble and describe local bosonic models. These Hamiltonians realize all discrete gauge theories and doubled Chern-Simons theories. The paper discusses the quasiparticle excitations of the string-net Hamiltonian, calculating their statistics and S matrix. The results show that string-net condensation provides a mechanism for unifying gauge bosons and fermions in 3 and higher dimensions. The paper concludes that string-net condensation provides a general theory of topological phases, with a mathematical framework of tensor categories and a physical picture of string-net condensation.String-net condensation is a physical mechanism for topological phases. Quantum systems of extended objects naturally give rise to a large class of exotic phases, namely topological phases, when these objects become highly fluctuating and condense. The authors derive exactly soluble Hamiltonians for 2D local bosonic models whose ground states are string-net condensed states. These ground states correspond to 2D parity invariant topological phases. The models reveal the mathematical framework underlying topological phases: tensor category theory. One of the Hamiltonians, a spin-1/2 system on the honeycomb lattice, is a simple theoretical realization of a fault tolerant quantum computer. In 3D, string-net condensation naturally gives rise to both emergent gauge bosons and fermions, unifying them in 3 and higher dimensions. The paper introduces the string-net picture in the context of gauge theory, showing that all deconfined gauge theories can be understood as string-net condensates. The authors argue that all doubled topological phases are described by string-net condensation. They construct fixed-point wave functions for each string-net condensed phase, which are associated with a six-index object satisfying certain algebraic equations. These wave functions capture the universal properties of the corresponding phases. The authors also construct fixed-point Hamiltonians for these phases, which are exactly soluble and describe local bosonic models. These Hamiltonians realize all discrete gauge theories and doubled Chern-Simons theories. The paper discusses the quasiparticle excitations of the string-net Hamiltonian, calculating their statistics and S matrix. The results show that string-net condensation provides a mechanism for unifying gauge bosons and fermions in 3 and higher dimensions. The paper concludes that string-net condensation provides a general theory of topological phases, with a mathematical framework of tensor categories and a physical picture of string-net condensation.