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This paper reports recent advances and open problems in navigation, control, and survey methodologies for underwater robotic vehicles. First, the technical challenges of underwater navigation are discussed. Second, an acoustic navigation system combining bottom-lock doppler sonar and time-of-flight long-baseline (LBL) navigation techniques, recently reported by the Authors, is reviewed. The performance of this system is examined in the context of recent deep-submergence operations with the Jason underwater robot. Third, principal theoretical and practical obstacles to the task of acoustic and optical undersea survey operations are reviewed. These issues are illustrated with acoustic bathymetric and optical photomosaic surveys performed by the authors during two recent deployments in the Mediterranean Sea.