A new cohesive micromechanical modeling framework is presented for the progressive damage analysis of laminated composite materials and structures. The framework is termed Cohesive Micromechanics and Progressive Analysis of Composites Theory (COMPACT). The COMPACT framework is a local-global damage modeling that recognizes the fiber and matrix constituents along with cohesive interface/interphase elements embedded between the fiber-matrix and matrix-matrix subcells. Traction-separation constitutive damage model is used for the cohesive subcells in order to degrade the traction and internal resisting force between the matrix and fiber subcells once damage or failure initiates. As a result, progressive damage modeling is achieved at the micromechanical level while maintaining the full advantage of using nonlinear micromechanical modeling prior and during damage progression. The proposed COMPACT damage framework approach allows nonlinear anisotropic response, including strain-softening, and damaged elastic loading/unloading behavior. Robust and efficient numerical stress correction algorithms have been also developed. The effectiveness of the proposed modeling approach is demonstrated by predicting the response of composite plates with an open hole under tension and compression loading using available test results from the literature.