The dynamics of red blood cells (RBCs) is one of the major aspects of the cardiovascular system that has been studied intensively in the past few decades. The dynamics of biconcave RBCs are thought to have major influences in cardiovascular diseases, the problems associated with cardiovascular assistive devices, and the determination of blood rheology and properties. This article provides an overview of the works that have been accomplished in the past few decades and aim to study the dynamics of RBCs under different flow conditions. While significant progress has been made in both experimental and numerical studies, a detailed understanding of the behavior of RBCs is still faced with many challenges. Experimentally, the size of RBCs is considered to be a major limitation that allows measurements to be performed under conditions similar to physiological conditions. In numerical computations, researchers still are working to develop a model that can cover the details of the RBC mechanics as it deforms and moves in the bloodstream. Moreover, most of reported computational models have been confined to the behavior of a single RBC in 2-dimensional domains. Advanced models are yet to be developed for accurate description of RBC dynamics under physiological flow conditions in 3-dimensional regimes.