Beyond classical laminate composites, woven polymer matrix composites are being considered for next-generation replacement materials in aerospace applications. In this regard, accurately predicting their ballistic performance and dynamic behavior is necessary, yet the influence of the matrix material on the continuum response due to the complex fiber-matrix interplay during damage evolution remains largely unknown. Carbon and glass fiber 2D woven composites with epoxy thermosetting resins are presented under quasi-static, dynamic, and biaxial dynamic compression in order examine strain rate and multi-axial loading state dependency. All materials and loading conditions and orientations exhibited localized shear band formation with characteristic geometry, and the results analyzed in the context of a Mohr-Coulomb failure theory. Inertial impact tests are conducted on carbon fiber woven composites using a single-stage gas-gun under non-uniform loading conditions. Utilizing ultra high-speed imaging with the full-field grid technique and the Virtual Field Method (and inverse identification method), the resulting displacement fields from the initial compression wave are used to extract the linear elastic orthotropic in-plane stiffness parameters, and the fracture and damage response is examined on the reflection of the wave on the downrange surface, loading the sample in dynamic tension to failure.