Chiral magnons are collective spin excitations whose dispersions break momentum inversion symmetry, $\omega(\boldsymbol{k}) \neq \omega(-\boldsymbol{k})$, leading to intrinsically nonreciprocal spin-wave propagation. This built-in directionality offers new opportunities for spin information transfer, thermal-spin interconversion, and low-dissipation nonreciprocal microwave devices, in a manner complementary to but distinct from topological magnonics. This review develops a unified framework for chiral magnons, covering symmetry-breaking mechanisms, material realizations, transport responses and many-body non-Hermitian dynamics, and evaluates routes toward room-temperature, device-relevant platforms. The discussion is based on symmetry analysis, model Hamiltonians and spin-wave theory, in combination with first-principles calculations and recent spectroscopic and transport measurements. The microscopic origins of chiral magnons are organized into three interrelated aspects, spin-orbit coupling (SOC)-driven Dzyaloshinskii-Moriya interactions (DMI) in non-centrosymmetric magnets and interfaces, altermagnetism in the weak SOC regime without DMI, and the spin space group (SSG) framework. On this basis, representative materials such as CrSb, α-MnTe, RuO₂ and MnF₂ are compared in terms of energy scales, coherence, momentum anisotropy and experimental visibility, clarifying how magnon splittings and lifetimes are reflected in direction-dependent spin Seebeck, spin Nernst and thermal Hall signals. The review further summarizes bulk-gap and Berry-curvature induced chiral edge states, enhancement of nonreciprocity via chiral spin pumping and cavity-magnon hybrids, and non-Hermitian features arising from multiparticle damping and gain-loss competition. Furthermore, remaining challenges, such as the stability of physical properties at room temperature, quantitative calibration of spectral and transport properties, as well as many-body competition also outlined. Finally, the possible strategies based on SSG-guided materials screening, multi-modal metrology and geometry phase engineering toward efficient spin logic, THz isolators and quantum routing based on chiral magnons also proposed.