This interdisciplinary thesis introduces a systems biology approach to study the cell fate decision mediated by autophagy. A mathematical model of interaction between Autophagy and Apoptosis in mammalian cells is proposed. In this dynamic model autophagy acts as a gradual response to stress (Rheostat) that delays the initiation of bistable switch of apoptosis to give the cells an opportunity to survive. The author shows that his dynamical model is consistent with existing quantitative measurements of time courses of autophagic responses to cisplatin treatment. To understand the function of this response in cancer cells, he has provided a systems biology experimental framework to study quantitative and dynamical aspects of autophagy in single cancer cells using live-cell imaging and quantitative fluorescence microscopy. This framework can provide new insights on function of autophagic response in cancer cells.