Current in vitro and in vivo models of cancer display certain limitations , which threaten the relevancy of the obtained data, and most importantly, impact in the selection of the most efficient therapy to be employed. Therefore, a new generation of personalised cancer models is needed, capable of predicting the response of individual cancer patients to a specific treatment. In this regard, organs-on-chip models of cancer, or cancer-on-a-chip, have emerged as powerful predictors for disease progression. These models can reproduce in a microfluidic chip the complex pathophysiology and interactions that occur in the native human scenario. They offer multiple advantages when compared to standard cancer models. This makes cancer-on-a-chip particularly interesting for clinical applications, and in particular, when tailored to the patient using primary cells, leading to highly personalised cancer patient-on-a-chip (CPoC) models. This new generation of CPoC models may be used to investigate, not only the mechanistic determinants of tumor progression, but also fundamental aspects of human physiology by linking together multiple organ models, such as the sequential metabolism of drug administration (adsorption, transport, excretion, toxicity) in the body, providing valuable information about drug toxicity and pharmacokinetics. Here we show the latest advances in the field of patient-on-a-chip models for personalised cancer medicine. We also put on display different in-house experiments of how organ-on-chip models may be used to develop functional CPoC. As an example, we employ a cancer-on-a-chip approach to analyze how A549 lung epithelial tumor cells embedded within 3D collagen matrices use invading protrusions and mechanical forces to invade a blood vessel-like microfluidic channel. Overall, CPoC models provide a unique biomimetic environment where to test personalised therapies. This provides highly valuable data about drug efficiency, side effects, and toxicity. Importantly, this precision medicine approach may help the physicians for taking decisions on the dynamic treatment regimes.