The manipulation and separation of particles and cells are crucial for disease diagnosis, biomedical research and therapeutic development. Microfluidics has shown significant progress in these areas, demonstrating precise manipulation and separation of tiny particles (e.g., cells, bacteria, viruses, and DNA). This technology offers advantages such as reduced sample volumes, lower cost, higher accuracy, automation and integration with multiple procedures. Among the various manipulation technologies, inertial microfluidics stands out due to its simple structure, label-free, easy operation, and high throughput. However, the current inertial microfluidic technology is still challenged when processing complex rare target cell samples, such as circulating tumour cells (CTCs) in blood samples. The separation efficiency and resolution are still limited. Moreover, conventional inertial microfluidic technology is difficult to handle heterogeneous cell samples, where particle sizes are too close or even partially overlap. Thus, it is urgent to develop innovative inertial microfluidic technology to enhance cell separation performance. [...]