The nature of the chemical bond is important in all natural sciences, ranging from biology to chemistry, physics and materials science. The atomic force microscope (AFM) allows to put a single chemical bond on the test bench, probing its strength and angular dependence. We review experimental AFM data, covering precise studies of van-der-Waals-, covalent-, ionic-, metallic- and hydrogen bonds as well as bonds between artificial and natural atoms. Further, we discuss some of the density functional theory calculations that are related to the experimental studies of the chemical bonds. A description of frequency modulation AFM, the most precise AFM method, discusses some of the experimental challenges in measuring bonding forces. In frequency modulation AFM, forces between the tip of an oscillating cantilever change its frequency. Initially, cantilevers were made mainly from silicon. Most of the high precision measurements of bonding strengths by AFM became possible with a technology transfer from the quartz watch technology to AFM by using quartz-based cantilevers ("qPlus force sensors"), briefly described here.