The past years have witnessed remarkable advances in our use of atomic force microscopy (AFM) for stretching single biomolecules, thereby contributing to answering many outstanding questions in biophysics and chemical biology. In these single-molecule force spectroscopy (SMFS) experiments, the AFM tip is continuously approached to and retracted from the biological sample, while monitoring the interaction force. The obtained force-extension curves provide key insight into the molecular elasticity and localization of single molecules, either on isolated systems or on cellular surfaces. In this tutorial review, we describe the principle of such SMFS experiments, and we survey remarkable breakthroughs made in manipulating single polysaccharides and proteins, including understanding the conformational properties of sugars and controlling them by force, measuring the molecular elasticity of mechanical proteins, unfolding and refolding individual proteins, probing protein-ligand interactions, and tuning enzymatic reactions by force. In addition, we show how SMFS with AFM tips bearing specific bioligands has enabled researchers to stretch and localize single molecules on live cells, in relation with cellular functions.