Circulating tumour cells (CTCs) are shed by primary tumours and are found in the peripheral blood of patients with metastatic cancers. Recent studies have shown that the number of CTCs corresponds with disease severity and prognosis. Therefore, detection and further functional analysis of CTCs are important for biomedical science, early diagnosis of cancer metastasis and tracking treatment efficacy in cancer patients, especially in point-of-care applications. Over the last few years, there has been an increasing shift towards not only capturing and detecting these rare cells, but also ensuring their viability for post-processing, such as cell culture and genetic analysis. High throughput lab-on-a-chip (LOC) has been fuelled up to process and analyse heterogeneous real patient samples while gaining profound insights for cancer biology. In this review, we highlight how miniaturisation strategies together with nanotechnologies have been used to advance LOC for capturing, separating, enriching and detecting different CTCs efficiently, while meeting the challenges of cell viability, high throughput multiplex or single-cell detection and post-processing. We begin this survey with an introduction to CTC biology, followed by description of the use of various materials, microstructures and nanostructures for design of LOC to achieve miniaturisation, as well as how various CTC capture or separation strategies can enhance cell capture and enrichment efficiencies, purity and viability. The significant progress of various nanotechnologies-based detection techniques to achieve high sensitivities and low detection limits for viable CTCs and/or to enable CTC post-processing are presented and the fundamental insights are also discussed. Finally, the challenges and perspectives of the technologies are enumerated.