We present a detailed density functional theory (DFT) based calculations of the structural, elastic, lattice dynamical, thermophysical, and optoelectronic properties of ternary semiconductors CaZn2X2 (X = N, P, As) in this paper. The obtained lattice parameters are in excellent agreement with the experimental values and other theoretical findings. The elastic constants are calculated. The computed elastic constants satisfy the mechanical stability criteria. Moreover, large numbers of thermophysical parameters of these compounds are estimated, including the Debye temperature, average sound velocity, melting temperature, heat capacity, lattice thermal conductivity, etc. The comprehensive analysis of the elastic constants and moduli show that CaZn2X2 (X = N, P, As) compounds possess reasonably good machinability, strongly X-dependent Debye temperature and high Vickers hardness. The phonon dispersion curves and phonon density of states are investigated for the first time for the compounds CaZn2P2 and CaZn2As2. It is observed from the phonon dispersion curves that the bulk CaZn2X2 (X = N, P, As) compounds are dynamically stable in the ground state. Electronic properties have been studied through the band structures and electronic energy density of states. HSE06 (hybrid) functional is used to estimate the band gaps accurately. The electronic band structures show that CaZn2N2 and CaZn2As2 possess direct band gaps while the compound CaZn2P2 has an indirect band gap. The bonding characters of CaZn2X2 (X = N, P, As) compounds are investigated. We have thoroughly discussed the reflectivity, absorption coefficient, refractive index, dielectric function, optical conductivity and loss function of these semiconductors. The optical absorption, reflectivity spectra and the refractive index of CaZn2X2 (X = N, P, As) show that they hold promise to be used in optoelectronic devices.