Frequency and phase estimation for carrier recovery in burst-mode coherent optical receivers are studied in this dissertation. Accurate models for frequency and phase deviations in communication lasers are initially studied, in order to present a tutorial study on frequency mismatch and phase recovery algorithms. Our studies take into account the current laser technology for optical communications using coherent receivers, especially the high short-term laser frequency stability for receivers operating above 100 Gbps. A special preamble design is presented for which an optimum estimator using the Minimum Mean-Square Error criterion is obtained. The estimator is given in closed-form solution with low computational space-and time-complexity. Simulation results in MatLab/Simulink are presented to validate the theoretical results.