Elementary quasiparticles in solids such as phonons and magnons occasionally have nontrivial interactions between them, as well as among themselves. As a result, their energy eigenvalues are renormalized, the quasiparticles spontaneously decay into a multi-particle continuum state, or they are hybridized with each other when their energies are close. As discussed in this review, such anomalous features can appear dominantly in quantum magnets but are not, a priori, negligible for magnetic systems with larger spin values and noncollinear magnetic structures. We review the unconventional magnetic excitations in two-dimensional triangular lattice antiferromagnets and discuss their implications on related issues.