This article highlights some physical studies on the relaxation dynamics and Förster resonance energy transfer (FRET) of semiconductor quantum dots (QDs) and the way these phenomena change with size, shape, and composition of the QDs. The understanding of the excited-state dynamics of photoexcited QDs is essential for technological applications such as efficient solar energy conversion, light-emitting diodes, and photovoltaic cells. Here, our emphasis is directed at describing the influence of size, shape, and composition of the QDs on their different relaxation processes, that is, radiative relaxation rate, nonradiative relaxation rate, and number of trap states. A stochastic model of carrier relaxation dynamics in semiconductor QDs was proposed to correlate with the experimental results. Many recent studies reveal that the energy transfer between the QDs and a dye is a FRET process, as established from 1/d6 distance dependence. QD-based energy-transfer processes have been used in applications such as luminescence tagging, imaging, sensors, and light harvesting. Thus, the understanding of the interaction between the excited state of the QD and the dye molecule and quantitative estimation of the number of dye molecules attached to the surface of the QD by using a kinetic model is important. Here, we highlight the influence of size, shape, and composition of QDs on the kinetics of energy transfer. Interesting findings reveal that QD-based energy-transfer processes offer exciting opportunities for future applications. Finally, a tentative outlook on future developments in this research field is given.