OOCs have emerged in the last years as the new frontier in high-throughput screening technology, in drug assessment and development, and in other domains such as nutraceutics, and cosmeceutics identification. OOCs hold the potential to reduce animal testing and provide realistic human cell and tissue in vitro assays [69]. The objective of OOC technology is not to build a complete living organ, but to synthesize minimal units that recapitulate the functions at the level of tissues and organs [38]. In general, the OOC is provided with culture compartments, often separated by a porous membrane, in which 3D tissues, often consisting of several cell types, can be cultured while microchannels assure nutrient supply. OOC takes advantage of the recent development of microfabrication techniques, and can be “custom-designed” to better mimic tissue-specific function. Through the right choice and the design of materials in the chips and the introduction of electrodes to deliver electrical/mechanical stimuli, it is possible to recapitulate the tissue-specific microenvironment and control the behavior of cells. At the same time, the microchannels provide the cells with the necessary nutrients and remove waste and can be precisely engineered to assure the 3D tissues with the correct (bio)chemical environment, as in the body [57]. A sort of classification of OOC can be made by identifying: OOC designed as single channel, compartmentalized, or membrane chips-based system (Figure 2). The complete chips are typically a few cm in size and made up by optically accessible plastic, glass, or flexible polymers [57]. In addition to the choice of materials, stimulation, and sensing, the cell sourcing represents a key issue in OOC technology. Cells used in OOC come from three main sources: cell lines, primary cells from human donors, and human induced pluripotent stem cells (hiPSCs). To date, by using hiPSCs, primary cells, and cell line, several tissues and/or organ types have been successfully modeled to reproduce corresponding functional subunits, including, for example, the brain [30], heart [70], lung [10,25,71], liver [26,27], intestine [72,73,74], vasculature [75,76,77], kidney [78]. Importantly, these OOC devices can reproduce organ level response to exogenous agents such as inflammatory responses of the lung to silica nanoparticles, [25] intestinal epithelial-microbiome crosstalk, [73] early liver fibrotic activation in response to anti metabolites chemotherapy drug [79] as well as flow dependent recruitment of circulating immune cells [80,81], and organ specific inflammatory reaction in vitro. Moreover, they can also effectively mimic many types of organ specific disease states, including pulmonary oedema and thrombosis, asthma, inflammatory bowel disease, paving the way for a new era in drug development and new therapeutic discovery [16,31]. As oncology is one of the most important targets of drug discovery, its is in this area that a number of advances in the creation of more physiologically relevant approaches, such as COC, are most evident [16,57,82]. The typology of the cells used to produce COC is similar to that used in OOC. COC often uses cell lines but resulting in inconsistencies between the model and an original tumor. This limitation can be solved with the use of patient biopsies that would generate PDX-tumor on chip models that would represent more powerful models than current ones, avoiding the use of established lines. Regarding the use of iPSC, it has emerged as the most promising candidate for OOCs since it can be produced from almost every type of adult cell, including skin-, blood-, or hair cells, and can be used to produce many different cell types that are present in various organs of the body, and that would otherwise be very difficult to obtain, such as cells from the heart, brain, lung, liver, gut, and also blood vessels. Despite this extensive use in OOC, we still have very few iPSC-based COC. The two most crucial bottlenecks in the establishment of iPSC cancer models are the efficiency of malignant-cell reprogramming and the ability to differentiate iPSCs into the cell type of interest. A few published studies and anecdotal reports suggest that cancer cells are generally more refractory to reprogramming than normal cells [83]. Several COC models have been developed in the last years allowing one to manipulate the TME for studying cell behavior under specific metabolic gradients conditions [84] or to study the TME changes correlated to CAF interaction and vice versa [16,21,40,85,86]. Controlled parameters and read-out methods can be different among chip types, but the read-outs are commonly based on cell and invasive lesion tracking, [87] gradient sensing, staining, and gene expression quantification using RT-qPCR [39]. The COC community has devoted significant attention to visualizing ECM components and remodeling, for which, thank to the optical accessibility of the microfluidic devices, different microscopy and imaging techniques can be used, such as second harmonic generation (SHG), confocal reflectance microscopy and immunofluorescence [39,88,89,90]. This enables simultaneous interrogation of ECM composition and structure with the measurement of transport parameters. This is particularly advantageous when cell synthesized matrices are used in the microfluidic devices, since provide a more representative tumor ECM allowing for the quantification of the contribution of each ECM constituent to transport properties [88,91,92]. Some of the earliest applications of microfluidic cell culture technology focused on modeling specific steps in the cancer cascade, including tumor growth and expansion, angiogenesis, progression from early to late stage lesions involving an EMT, tumor cell invasion and metastasis. Here, we concentrate our attention on COC designed for recreating tissue–tissue interfaces, crucial for reconstituting in a physiological context the interaction occurring between tumor and its environment during cancer invasion and metastasis. Owing to several other interesting reviews looking into tumor chips including endothelial and immune cells [17,19,93,94,95] we do not discuss the tumor–endothelial–immune cells interactions in this paper but mainly debate cancer-cell–ECM interactions during tumor growth and invasion, focusing on the role of biophysical properties of ECM in guiding the pathological tumoral process.