Modern electronics is based on semiconductor nanostructures in practically all main parts: from microprocessor circuits and memory elements to high frequency and light-emitting devices, sensors and photovoltaic cells. Metal-Oxide-Semiconductor Field-Effect Transistor (MOSFET) with ultimately low gate length in the order of tens of nanometers and less is nowadays one of the basic elements of microprocessors and modern electron memory chips. Principally new physical peculiarities of semiconductor nanostructures are related to quantum effects like tunneling of charge carriers, controlled changing of energy band structure, quantization of energy spectrum of a charge carrier and a pronounced spin-related phenomena. Superposition of quantum states and formation of entangled states of photons offers new opportunities for the realization of quantum bits, development of nanoscale systems for quantum cryptography and quantum computing. Advanced growth techniques such as molecular beam epitaxy and chemical vapour epitaxy, atomic layer deposition as well as optical, electron and probe nanolithography for nanostructure fabrication have been widely used. Nanostructure characterization is performed using nanometer resolution tools including high-resolution, reflection and scanning electron microscopy as well as scanning tunneling and atomic force microscopy. Quantum properties of semiconductor nanostructures have been evaluated from precise electrical and optical measurements. Modern concepts of various semiconductor devices in electronics and photonics including single-photon emitters, memory elements, photodetectors and highly sensitive biosensors are developed very intensively. The perspectives of nanostructured materials for the creation of a new generation of universal memory and neuromorphic computing elements are under lively discussion. This paper is devoted to a brief description of current achievements in the investigation and modeling of single-electron and single-photon phenomena in semiconductor nanostructures, as well as in the fabrication of a new generation of elements for micro-, nano-, optoelectronics and quantum devices.