Microfluidic organ-on-chip systems are promising platforms for the development of biomimetic models that aim to reconstruct the 3D architecture and intrinsic functionality of native tissues. An in-depth comprehension of the pivotal role of extracellular matrix in intricate cellular responses has paved the way for the emergence of biologically-relevant and instructive biomaterials that can capture the essence of the cell's microenvironment. The notable evolution in the realm of biomaterials toward the development of more realistic 3D in vitro tissue models capable of recreating the synergistic cell-extracellular matrix interplay is covered. An overview of the most recent advances in integrating biomimetic materials into organ-on-chip systems is provided, including the exploitation of bulk hydrogels as soft material devices to fulfill the requirements for direct cell-matrix interaction. The successful application of this cutting-edge technology on tumor modeling is then discussed, highlighting the great contribution of perfusable microvessels to elucidate the mechanistic events of tumor metastatic cascade. This convergence of biomaterials science with organ-on-a-chip technology is envisioned to foster the understanding of native cellular behavior, shedding light on the dynamism of cell-extracellular matrix interactions.