Red blood cells (RBCs) play a crucial role in health and disease, and structural and mechanical abnormalities of these cells have been associated with important disorders such as Sickle cell disease and hereditary cytoskeletal abnormalities. Although several experimental methods exist for analysis of RBC mechanical properties, optical methods stand out as they enable collecting mechanical and dynamic data from live cells without physical contact and without the need for exogenous contrast agents. In this report, we present quantitative phase microscopy techniques that enable imaging RBC membrane fluctuations with nanometer sensitivity at arbitrary time scales from milliseconds to hours. We further provide a theoretical framework for extraction of membrane mechanical and dynamical properties using time series of quantitative phase images. Finally, we present an experimental approach to extend quantitative phase imaging to 3-dimensional space using tomographic methods. By providing non-invasive methods for imaging mechanics of live cells, these novel techniques provide an opportunity for high-throughput analysis and study of RBC mechanical properties in health and disease.