The long dreamed 'quantum internet' would consist of a network of quantum nodes (solid-state or atomic systems) linked by flying qubits, naturally based on photons, travelling over long distances at the speed of light, with negligible decoherence. A key component is a light source, able to provide single or entangled photon pairs. Among the different platforms, semiconductor quantum dots (QDs) are very attractive, as they can be integrated with other photonic and electronic components in miniaturized chips. In the early 1990s two approaches were developed to synthetize self-assembled epitaxial semiconductor QDs, or 'artificial atoms'-namely, the Stranski-Krastanov (SK) and the droplet epitaxy (DE) methods. Because of its robustness and simplicity, the SK method became the workhorse to achieve several breakthroughs in both fundamental and technological areas. The need for specific emission wavelengths or structural and optical properties has nevertheless motivated further research on the DE method and its more recent development, local droplet etching (LDE), as complementary routes to obtain high-quality semiconductor nanostructures. The recent reports on the generation of highly entangled photon pairs, combined with good photon indistinguishability, suggest that DE and LDE QDs may complement (and sometimes even outperform) conventional SK InGaAs QDs as quantum emitters. We present here a critical survey of the state of the art of DE and LDE, highlighting the advantages and weaknesses, the achievements and challenges that are still open, in view of applications in quantum communication and technology.