Chiral magnons are distinctive collective spin excitations in magnetic ordered systems, whose dispersion relations break momentum-inversion symmetry, \omega (\boldsymbolk)\neq \omega (-\boldsymbolk) , resulting in essential non-reciprocal spin-wave propagation. This built-in directionality provides new opportunities for spin information transfer, thermal-spin interconversion, and low-dissipation non-reciprocal microwave devices, which complement but differ from topological magnonics. In recent years, the proposal and rapid development of altermagnetism have broadened the physical origin and research framework of chiral magnons, making them a research frontier in condensed matter physics. This review presents a unified framework for chiral magnons, covering symmetry-breaking mechanisms, material implementation, experimental characterization, transport response, and many-body non-Hermitian dynamics, and evaluates routes toward room-temperature and device-related platforms. The discussion is based on symmetry analysis, model Hamiltonians, and spin-wave theory, combined with first-principles calculations as well as recent spectroscopic (e.g., inelastic and polarized neutron scattering, Brillouin light scattering) and transport measurements. The microscopic origins of chiral magnons can be divided 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; the spin space group (SSG) framework. On this basis, representative materials such as CrSb, α-MnTe, α-Fe₂O₃, RuO₂, and MnF₂ are compared in terms of magnetic order and type, physical mechanism, chiral energy scale, coherence, momentum anisotropy, test temperature, and experimental visibility, clarifying how magnon dispersion splitting and lifetimes are reflected in direction-dependent spin Seebeck effects, spin Nernst effects, and thermal Hall signals. At the level of non-reciprocal propagation and device applications, chiral magnons are evolved from intrinsic material properties to artificially engineerable system-level functionalities, thereby paving the way for practical non-reciprocal magnonic devices. This review further summarizes bulk-gap and Berry-curvature induced chiral magnon edge states, the enhancement of non-reciprocity via chiral spin pumping and cavity-magnon hybrids, as well as non-Hermitian features arising from multiparticle damping and gain-loss competition. Besides, 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, are also outlined. Finally, possible strategies based on SSG-guided material screening, multi-modal metrology, and geometry phase engineering toward efficient spin logic, THz isolators, and quantum routing based on chiral magnons are proposed. This review provides a comprehensive reference for elucidating the underlying mechanisms of chiral magnons, advancing the synthesis and experimental characterization of novel materials, and also guiding the design of next-generation non-reciprocal magnonic devices.