While the presence of random fluctuations has been increasingly predicted and ob served in many cellular processes, there has been relatively little appreciation of how entirely deviant the behaviors of stochastic biological systems could be from those expected via traditional deterministic descriptions. As a result, th e effects of noise can often play important yet altogether non-intuitive roles i n shaping cell physiology, including in such biomedically-relevant settings as i nfectious diseases, cancer, normal or pathological tissue development and differ entiation, etc. My talk will discuss a rigorous modeling and simulation framewor k for tracing the effects and causes of such deviant behaviors based on the disc rete and stochastic nature of underlying cellular biochemistry. As an example, I will demonstrate how our approach can be used to better understand and explain data from Hematopoietic stem cells and immune cells as well as to obtain additio nal insights into other syste ms spanning gene expression and signal transduction. Finally, I will discuss the broader implications of such noisy mechanisms for organismal physiology, fitnes s and phenotypic variability.