Parametrically Homogenized Continuum Damage Mechanics (PHCDM) models are developed to simulate multi-scale damage and failure phenomena in composites. Starting from detailed micromechanical models, macroscopic constitutive equations for connecting micro-macro material behaviors are established through parametric homogenization, energy equivalence and thermodynamic principles, along with extensive data analysis and physics-informed machine learning. The developed PHCDM model exhibits the capabilities of both micromechanical models and conventional continuum damage approaches: through functional incorporation of representative aggregated microstructural parameters (RAMPs), it explicitly accounts for the effects of important microstructural features on material behaviors, meanwhile it is computationally efficient to be deployed in structural analysis. These advantages of PHCDM framework helps understand damage behaviors across different material length scales with affordable computational effort, and can significantly facilitate the material-by-design process. PHCDM models can be easily implemented as user-subroutines (UMAT/VUMAT) in any commercial FEM packages for performing structural-scale analysis. Some example problems and experimental comparisons will be presented to demonstrate the capabilities of PHCDM.