Semiconductor alloy nanowires with spatially graded compositions (and bandgaps) provide a new material platform for many new multifunctional optoelectronic devices, such as broadly tunable lasers, multispectral photodetectors, broad-band light emitting diodes (LEDs) and high-efficiency solar cells. In this review, we will summarize the recent progress on composition graded semiconductor alloy nanowires with bandgaps graded in a wide range. Depending on different growth methods and material systems, two typical nanowire composition grading approaches will be presented in detail, including composition graded alloy nanowires along a single substrate and those along single nanowires. Furthermore, selected examples of applications of these composition graded semiconductor nanowires will be presented and discussed, including tunable nanolasers, multi-terminal on-nanowire photodetectors, full-spectrum solar cells, and white-light LEDs. Finally, we will make some concluding remarks with future perspectives including opportunities and challenges in this research area.