In recent years, remarkable advances in research of the mechanical and structural properties of single polymer chains have been achieved thanks to atomic force microscope (AFM)-based single molecule force spectroscopy (SMFS). This technique offers great possibilities to investigate the mechanical properties of a single polymer chain by static/dynamic force-extension measurements at the mesoscale level. Data are analyzed with the help of appropriate theoretical models, such as statistical mechanics models for freely jointed chains (FJC) or worm-like chains (WLC), which can well describe the moderate entropy-controlled stretch of most polymers, and with semiclassical models, which are being modified using quantum mechanics principles to account for entropic and enthalpic contributions to stretching in the high-force Hookean regime. In this article we review the theoretical models of single chain stretching, the latest progress in force-extension measurements by static and dynamic AFM modes for polymer chains dispersed in different solvents and subjected to a force that may induce their conformational transformations, as well as relevant applications.