Over the past few decades, microfluidics has emerged as an extensive and multidisciplinary area of research within the domain of fluid dynamics. The rise in technological advancements especially in the field of electronics and instrumentation has resulted in the development of microfluidics based biomedical devices and techniques for diagnosis, vital monitoring, support systems, and therapeutic screening. The contribution of fluid dynamics to biomedical engineering range from the fundamental understanding of physiological flows to the design and development of blood pumps and dialysis units. Microfluidics comes handy due to its inherent advantages in sensing, sample requirements, time of detection and the affordability to the masses. In the light of these developments in the field of microfluidics with potential applications in areas ranging from soft matter physics to global healthcare, my research studies were focused on experimental and theoretical aspects of fluid flows in deformable microchannels that mimic the human vasculature. I have fabricated deformable microchannels using microfabrication techniques and the hydrodynamic studies were conducted using fluorescent microscopy, pressure probing and micro–Particle Image Velocimetry. The experimental results, corroborated with theoretical analysis have demonstrated the intricate relationship of the channel deformation and the pressure drop across a deformable microchannel. Later, I have also experimented with time varying flows and flows of RBCs in deformable microchannels. Presently, I am exploring the fundamental and applied aspects of transport phenomena at microscale with emphasis on problems of high socioeconomic relevance like cost-effective platforms for cancer drug screening.