This thesis describes the physics and applications of quantum dot semiconductor optical amplifiers based on numerical simulations. These devices possess a number of unique properties compared with other types of semiconductor amplifiers, which should allow enhanced performance of semiconductor devices in communication systems in the future. The basic properties of quantum dot devices are investigated, especially regarding the potential of realizing amplification and signal processing without introducing pattern dependence. Also the gain recovery of a single short pulse is modeled and an explanation for the fast gain recovery observed experimentally is given. The properties of quantum dot amplifiers operating in the linear regime are investigated. The devices are predicted to show high device gain, high saturated output power, and low noise figure, resulting in a performance, that in some respects is comparable to those of fiber amplifiers. The possibility of inverting the optically active states to a large degree is essential in order to achieve this performance. Optical signal processing through cross gain modulation and four wave mixing is modeled and described. For both approaches quantum dot amplifiers are found to be able to operate with high efficiency and at high bitrates. Strong spectral hole-burning arising from a relatively slow carrier capture time, is shown to play a dominant role is this context. The results obtained numerically are compared to the properties of bulk and QW devices and to experiments on quantum dot amplifiers. These comparisons outline the qualitative differences between the different types of amplifiers. In all cases focus is put on the physical processes responsible the differences.