The proteins’ phase transition dynamics challenged researchers for the last few decades and it continues to generate increasing interest. This problem requires a detailed deterministic knowledge of the kinetics of the phase transition, as well as statistical - mechanical treatments trying to capture the nucleation and propagation steps of folding. Until recently there was also an important technology barrier which delayed the analysis of the complex behavior of these reactions occurring within nanosecond time frames scale. In this talk I will give an introduction to some basic aspects of mathematical modeling in protein folding. Specific topics will include: a brief description of the statistical mechanical model of Zimm and Bragg as indicative for the cooperativity of the phase transition in biopolymers; deterministic models for the dynamic cooperativity parameter in helix - coil transitions; deterministic models leading to self - sustained and damped oscillations in single molecule folding/unfolding kinetics. The possibility of experimental validation of the theoretical modeling - by spectroscopic techniques - will be discussed, too.