Using scanning probe microscopy techniques, at low temperatures and in ultrahigh vacuum, individual molecules adsorbed on surfaces can be probed with ultrahigh resolution to determine their structure and details of their conformation, configuration, charge states, aromaticity, and the contributions of resonance structures. Functionalizing the tip of an atomic force microscope with a CO molecule enabled atomic-resolution imaging of single molecules, and measurement of their adsorption geometry and bond-order relations. In addition, by using scanning tunneling microscopy and Kelvin probe force microscopy, the density of the molecular frontier orbitals and the electric charge distribution within molecules can be mapped. Combining these techniques yields a high-resolution tool for the identification and characterization of individual molecules. The single-molecule sensitivity and the possibility of atom manipulation to induce chemical reactions with the tip of the microscope open up unique applications in chemistry, and differentiate scanning probe microscopy from conventional methods for molecular structure elucidation. Besides being an aid for challenging cases in natural product identification, atomic force microscopy has been shown to be a powerful tool for the investigation of on-surface reactions and the characterization of radicals and molecular mixtures. Herein we review the progress that high-resolution scanning probe microscopy with functionalized tips has made for molecular structure identification and characterization, and discuss the challenges it will face in the years to come.