This dissertation addresses attitude control and inertial navigation of autonomous underwater vehicles (AUVs). We present theoretical justification for using simplified models, derive system identification algorithms, and verify our results through extensive field trials. Although this research focuses on small AUVs with limited instrumentation, the results are useful for underwater vehicles of any size. For attitude control of aircraft systems, second-order equivalent pitch-axis models are common and extensively studied. However, similar analysis has not been performed for the pitch-axis motion of underwater vehicles. In this dissertation, we study the utility and the limitations of second-order approximate models for AUVs. We seek to improve the flight performance and shorten the time required to re-design a control algorithm when the shape, mass-distribution, and/or net buoyancy of an AUV/payload configuration changes. In comparison to commonly implemented AUV attitude controllers, which neglect roll motion and address pitch and yaw dynamics separately, we derive a novel linear time-varying model that explicitly displays the coupling between pitch and yaw motion due to nonzero roll angle and/or roll rate. The model facilitates an Hâ control design approach that explicitly addresses robustness against those coupling terms and significantly reduces the effect of pitch and yaw coupling. To improve AUV navigation, we investigate algorithms for calibrating a triaxial gyroscope using angular orientation measurements and formally define AUV trajectories that are persistently exciting and for which the calibration coefficients are uniformly observable. To improve AUV guidance, we propose a near real-time ocean current identification method that estimates a non-uniform flow-field using only sparse flow measurements. / Ph. D.