Recent experimental and theoretical investigations of frustrated triangular-lattice antiferromagnets are reviewed. An analysis is made of phases with different structures: partly disordered and double incommensurate states, helical configurations, triangular superstructures, etc. These phases appear because of an instability of the conical high-symmetry point in the Brillouin zone as a result of the dipole interaction, or they may be due to other factors. An analysis is made of magnetic transitions belonging to new universal classes as well as Berezinskii--Kosterlitz--Thouless transitions with an exponential decay of correlations in the low-temperature phase. The chiral symmetry and the associated problem of transition accompanied by simultaneous ordering of discrete and continuous components of the order parameter space are considered for triangular antiferromagnets with different spins. The spectrum of collective modes of some incommensurate structures is analyzed.