In this article, recent developments in the lattice‐mismatched epitaxy of InAs on (111)A‐oriented substrates and related research topics, in which the presence or absence of the misfit dislocations is controlled via prescribed growth sequences, are reviewed. When InAs is grown on GaAs (111)A substrates, a unique lattice‐relaxation mechanism occurs. A misfit dislocation network is formed at the initial stage of InAs growth, that is followed by the layer‐by‐layer growth of relaxed InAs films. The InAs/GaAs (111)A heterostructure is being applied in infrared photodetectors which have a new operating principle that employs the high‐density dislocations at the interface. The InAs/GaAs (111)A heterostructure is also useful for the growth of InGaAs layers: a nearly lattice‐relaxed InGaAs containing different concentrations of indium can be formed by inserting a thin‐InAs layer between the InGaAs and GaAs. These InGaAs layers can be used as virtual substrates with a desired lattice constant for a range of devices. In addition to the formation of lattice‐relaxed structures, dislocation‐free InAs quantum dots (QDs) can be formed on InP (111)A substrates by applying droplet epitaxy. The C3v symmetry of the (111)A surface makes it possible to form symmetric InAs QDs that emit entangled photon pairs at telecommunication wavelengths.