The properties of a given molecule or nanoscale structure are conventionally characterized by its mean value that is averaged over a great number of molecules (N~1023). Such an ensemble-averaged description becomes inadequate, however, as the number of molecules under consideration decreases where the observable range of fluctuation approximately scales with N-1/2. To an observer in the macroscopic world, the changes in the microscopic states as a function of time and location are no longer deterministic but probabilistic. The central premise of the current research thrust is that these local stochastic fluctuations give rise to the chemical and physical transformations as they appear in the macroscopic world. This general problem is studied at the most fundamental, single-molecule and single-particle level. New experimental approaches are devised to enable real-time observations of individual molecules as they move and function. Theoretical frameworks are concurrently formulated to afford a quantitative understanding.