Fiber-polymer composites consist of a polymer matrix and reinforcing fibers made of various materials. These composites exhibit exceptional properties, such as a high strength-to-weight ratio and excellent corrosion resistance, which has led to their increasing use in diverse engineering fields. Typically featuring a layered structure, they demonstrate different failure modes compared to conventional construction materials like concrete and metals. In particular, the weaker properties in the thickness direction make them prone to the separation between layers, i.e., delamination. The study of delamination failure has been a focal point for researchers in the past decades, prompting the establishment of several test standards to assess the material's resistance to delamination. These tests typically involve one-dimensional (1D) beam specimens with a pre-crack subjected to specific fracture mode or mixed mode conditions. While these approaches are valuable for analysis due to the relative simplicity in the test set-up and the stress state of the specimen, they do not capture the actual delamination behavior of cracks embedded in laminates, which tend to propagate in multiple directions with varying contours. To investigate the delamination fracture behavior of laminates in a more realistic context and uncover potential two-dimensional (2D) effects, in this research, the 2D delamination growth is investigated and compared with traditional 1D fracture tests. Under the context of Mode-I fracture conditions, previous experiments have preliminarily attributed the main differences between 2D and 1D delamination behaviors to the increasing crack-front length and the membrane forces (stretching) occurring during large plate-deformation. Based on these experimental results, a numerical investigation of the 2D delamination growth was conducted using the cohesive zone method (CZM), exploring the influences of a variety of parameters including the pre-crack shape/area, loading-zone shape/area and fracture resistance. In the case of 2D Mode-II delamination, experimental investigations were conducted on two groups of plate specimens with central pre-cracks of different sizes. The specimens were subjected to transverse loading and semi-clamped along the edge, allowing in-plane sliding while constraining rotation and out-of-plane movement along the edge. An increase in the crack propagation rate occurred, while the load continued to increase until flexural failure. Under post-inspection with a digital microscope, a long fracture process zone, including large-scale fiber bridging and hackles reflecting microcracks, was observed. To further investigate the 2D effects on the fracture mechanisms in the Mode-II experiments, a novel cohesive model, considering both the microcracking and fiber bridging, was employed for finite element analysis (FEA). Although the maximum SERR was similar in 2D and end-loaded split (ELS) experiments, the mean traction stresses over the microcracking zone were notably lower in 2D delamination due to the overall tensile membrane forces induced by large deformation. Practical methods for locating the crack tip of an embedded crack based on surface measurements, such as the curvature and strains, were proposed.