Knowing excitonic and biexcitonic properties of low-dimensional semiconductors systems is extremely important for the discovery of new physical effects and for the development of novel optoelectronics applications. This review work furnishes an interdisciplinary analysis of the fundamental features of excitons and biexcitons in two-dimensional semiconductor structures, one-dimensional semiconductor structures, and zero-dimensional (0D) semiconductor structures. There is a focus on spectral and dynamical properties of excitons and biexcitons in quantum dots (QDs). A study of the recent advances in the field is given, emphasizing the latest theoretical results and latest experimental methods for probing exciton and biexciton dynamics. This review presents an outlook on future applications of engineered multiexcitonic states including the photovoltaics, lasing, and the utilization of QDs in quantum technologies.