Recent advances in nano-technology allow scientists for the first time to follow a biochemical process on a single molecule basis. These advances also raise many challenging data-analysis problems and call for a sophisticated statistical modeling and inference effort. First, by zooming in on single molecules, recent single-molecule experiments revealed that many classical models derived from oversimplified assumptions are no longer valid. Second, the stochastic nature of the experimental data and the presence of latent processes much complicate the inference. In this talk we will use the modeling of subdiffusion phenomenon in enzymatic reaction to illustrate the statistics and probability challenges in single-molecule biophysics. This talk is based on joint work with Sunney Xie. \bigskip \bf \it Jointly sponsored by the Department of Mathematics and the Division of Biostatistics and Bioinformatics