Ab initio density-functional-theory-local-density-approximation electronic structure calculations are performed for the InAs(110) surface and compared with scanning tunnel microscopy (STM) measurements using the Tersoff-Hamann model. In both, calculations and measurements, we see the same atomic features. At negative and small positive energies, the local density of states is concentrated around the As atom, while at higher positive energies it is centered above the In atom, because of the appearance of the In dangling bond. Moreover, we describe two types of irregular STM images on the InAs(110) surface. First, we measure dI/dV images exhibiting atomic resolution at voltages within the band gap, which, however, still can be understood within the Tersoff-Hamann model as due to a higher-order term. Second, we measure features on the subatomic scale with certain tips at low tip-sample distance, which are most likely caused by elastic interactions between the tip and the surface.