Biophysical (mechanical and electrical) properties of living cells have been proven to play important roles in the regulation of various biological activities at the molecular and cellular level, and can serve as promising label-free markers of cells' physiological states. In the past two decades, a number of research tools have been developed for understanding the association between the biophysical property changes of biological cells and human diseases; however, technical challenges of realizing high-throughput, robust and easy-to-perform measurements on single-cell biophysical properties have yet to be solved. In this paper, we review emerging tools enabled by microfluidic technologies for single-cell biophysical characterization. Different techniques are compared. The technical details, advantages, and limitations of various microfluidic devices are discussed.