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 similar “robust” conducting edge states can be implemented in classical systems. In this talk I will review development of this field with focus on photonic and acoustic topological structures with and without time-reversal symmetry that we have recently proposed. I will discuss recent experimental realizations of topological order for electromagnetic waves with the use of bianisotropic metamaterials at microwave frequencies. New practical designs of photonic and acoustic topological insulators and their possible applications will be presented. I will show that photonic and acoustic topological systems, with deliberately created distributions of synthetic gauge fields, offer an unprecedented platform for controlling light and sound, e.g. by enabling routing and steering of waves along arbitrarily shaped pathways without loss or backscattering.