The past three decades have witnessed the discovery of Quantum Hall Effect (QHE), Quantum Spin Hall Effect (QSHE) and Topological Insulators (TIs), which transformed our views on the quantum states of matter. These exotic states are characterized by insulating behavior in the bulk and the presence of the edge states contributing to charge or spin currents which persist even when the edge is distorted or contains impurities. In the last few years, a number of studies have shown that the same “robust” conducting edge states can be implemented in classical systems. An early theoretical prediction and experimental demonstration of the topologically protected transport of light opened a new direction in photonics. In this talk I will review development of this field with focus on photonic and acoustic topological metamaterials with and without time-reversal symmetry that we have recently proposed. I will also discuss recent experimental realizations of topological order for electromagnetic waves with the use of bianisotropic metamaterials at microwave frequencies [Nature Materials 12, 233 (2013)]. New practical designs of photonic and acoustic topological insulators will be presented and perspectives of their applications will be discussed. It will be shown that photonic and acoustic topological systems offer an unprecedented platform for controlling light and sound: deliberately created distribution of synthetic gauge fields allows routing of waves along arbitrary pathways without loss or backscattering [Nature Photonics 7, 941 (2013)].