Autonomous Underwater Vehicles (AUVs) represent a very promising tool for high resolution bathymetric surveys. In this context, this article presents a state-of-the-art of precise underwater navigation. While classical acoustic underwater positioning systems (USBL, LBL) provide a sufficient level of precision, they suffer from deployment difficulties: beacons immersion, need for support vessel, etc.. Therefore these methods are not further developed in this article and a conventional underwater navigation method consists in inertial navigation. However, position accuracy of inertial systems drifts over time, making it incompatible with bathymetric survey quality requirements for long missions. To limit this drift, external speed sensors (a Doppler Velocity Log-DVL-most of the time) are used: this is called Aided Inertial Navigation System (AINS). AINS performances depend on sensor performances, data fusion algorithms and mission pattern followed by the AUV. These considerations are presented in this paper and illustrated by two sea trials conducted in the bay of Brest (France). Finally, Terrain Based Navigation (TBN), Simultaneous Localization And Mapping (SLAM) and Synthetic Aperture Sonar (SAS) micronavigation are presented as emerging methods that could help to reduce or bound the position uncertainty drift.