We propose a three-dimensional (3D) imaging platform based on lens-free microscopy to perform multi-angle acquisitions on 3D cell cultures embedded in extracellular matrix (ECM). We developed algorithms based on the Fourier diffraction theorem to perform fully 3D reconstructions of biological samples and we adapted the lens-free microscope to incubator conditions. Here we demonstrate for the first time, 3D+time lens-free acquisitions of 3D cell culture over 8 days directly into the incubator. The 3D reconstructed volume is as large as ~5 mm3 and provides a unique way to observe in the same 3D cell culture experiment multiple cell migration strategies. Namely, in a 3D cell culture of prostate epithelial cells embedded within a Matrigel® matrix, we are able to distinguish single cell ’leaders’, migration of cell clusters, migration of large aggregates of cells, and also close-gap and large-scale branching. In addition, we observe long-scale 3D deformations of the ECM that modify the geometry of the 3D cell culture. Interestingly, we also observed the opposite, i.e. we found that large aggregates of cells may deform the ECM by generating traction forces over very long distances. In sum we put forward a novel 3D lens-free microscopy tomographic technique to study the single and collective cell migrations, the cell-to-cell interactions and the cell-to-matrix interactions.