Recent progress in atomic force microscopy (AFM) technology has allowed the measurement of inter- and intramolecular forces at the level of individual molecules. The mechanical manipulation of single polymer chains immobilized on solid substrates has become possible in solution, as they are spanned and stretched between the tip of an AFM cantilever and the substrate surface. This investigation of polymer chains far from their maximum entropy configurations has stimulated the refinement of existing polymer theories. From the measured force-distance curves quantitative information can be obtained on the elasticity of single macromolecules in solution, on conformational transitions along the chains, about the mechanical stability of chemical bonds and on secondary structures, as well as on the desorption of individual polymer molecules from solid substrates. Recent applications of AFM single molecule force spectroscopy reach from the study of dynamic processes in complex biological systems and intermolecular forces in colloidal systems to the investigation of new functional materials capable of performing energy transductions on the level of individual macromolecules. In this article, we present a detailed description of the experimental procedure, followed by an overview of the development, the success and the current challenges of this technique during the past five years, in which it has rapidly evolved from the first proof of principle to a highly active field of research.