We discuss experimental results on the spatial and time resolved photoluminescence in quantum wires and dots using a micro-photoluminescence technique. Particularly, we succeeded in measuring time resolved photoluminescence from a single quantum dot. Very fast diffusion dynamics of excitons in the quantum wires were observed as well as long photoluminescence decay times in a single quantum dot. These results demonstrate the one-dimensional and zero-dimensional characters of excitons in the quantum nanostructures.