This thesis describes the physics and applications of quantum dot semiconductor optical ampliers through numerical simulations. As nano-structured materials with zero-dimensional quantum connement, semiconductor quantum dot material provides a number of unique physical properties compared with other semiconductor materials. The understanding of such properties is important in order to improve the performance of existing devices and to trigger the development of new semiconductor devices for dierent optical signal processing functionalities in the future. We present a detailed quantum dot semiconductor optical amplier model incorporating a carrier dynamics rate equation model for quantum dots with inhomogeneous broadening as well as equations describing propagation. A phenomenological description has been used to model the intradot electron scattering between discrete quantum dot states and the continuum. Additional to the conventional time-domain modeling scheme, a small-signal perturbation analysis has been used to assist the investigation of harmonic modulation properties. The static properties of quantum dot devices, for example high saturation power, have been quantitatively analyzed. Additional to the static linear amplication properties, we focus on exploring the gain dynamics on the time scale ranging from sub-picosecond to nanosecond. In terms of optical signals that have been investigated, one is the simple sinusoidally modulated optical carrier with a typical modulation frequency range of 1-100 gigahertz. Our simulations reveal the role of ultrafast intradot carrier dynamics in enhancing modulation bandwidth of quantum dot semiconductor optical ampliers. Moreover, the corresponding coherent gain response also provides rich dispersion contents over a broad bandwidth. One important implementation is recently boosted by the research in slow light. The idea is to migrate such dynamical gain knowledge for the investigation of microwave phase shifter based on semiconductor optical waveguide. Our study reveals that phase shifting based on the conventional semiconductor optical amplier is fundamentally limited over a narrow bandwidth determined by the slow carrier density pulsation processes. In contrast, we predict that using quantum dots as the active material instead can provide bandwidth enhancement even beyond 100 gigahertz due to its unique extra ultrafast carrier dynamics. We also investigate the gain dynamics in the presence of pulsed signals, in particular the steady gain response to a periodic pulse trains with various time periods. Additional to the analysis of high speed patterning free amplication up to 150-200 Gb/s in quantum dot semiconductor optical ampliers, we discuss the possibility to realize a compact high-speed all-optical regenerator by incorporating a quantum dot absorption section in an amplier structure.