An overview on strain-free semiconductor quantum ring (QR) structures is given that are created in a self-assembled fashion with the local droplet etching (LDE) method. LDE is fully compatible with conventional molecular beam epitaxy (MBE) and utilizes liquid Ga or Al droplets which drill nanoholes into semiconductor surfaces. The nanohole openings are surrounded by walls composed of Arsenides of the droplet material. Here the nanohole and wall formation mechanisms and the tunability of their structural properties are discussed. Two different concepts for QR generation by LDE are addressed. In the first concept, recrystallized GaAs builds ring-like walls around the nanohole openings during LDE with Ga droplets on AlGaAs substrates. These crystalline GaAs walls form directly QRs. The second concept is based on V-shaped GaAs QDs that are created by filling of nanoholes drilled using LDE with Al droplets into AlGaAs with GaAs. The unique shape of the V-shaped QDs allows for a strong wave-function tuning by a vertical electric field. In particular the hole wave function can be transformed into a ring-shape whereas the electron remains in a zero-dimensional QD state. To our knowledge, this asymmetric strong-weak confinement represents a novel kind of quantum mechanical confinement and has not been observed so far. The fabrication and structural properties of both types of QRs, optical data, and simulations of the quantized electronic levels and wave functions are discussed. Finally, for V-shaped QDs in combined vertical electric and magnetic fields, optical Aharonov-Bohm oscillations and an application as a storage for photo-excited charge carriers are predicted.