The aim of this report is to discuss signatures from surface ships and submarines from a general perspective, and to tie that our present knowledge of the flow past surface ships and submarines. The study is motivated by the increased interest in determining signatures for domestic and alien vessels. There is a significant interest in reducing or minimizing signatures from domestic vessels and to know how various signatures change under different environmental, operating and tactical conditions. This is particularly important to submarines operating in litorial waters, but is becoming more and more important also to surface ships. In addition, there is interest in developing or modifying capabilities and methods for estimating signatures for alien vessels - in operation as well as under construction. Besides experiments in full or model scale computational fluid dynamics offers an interesting alternative in that simulations ca be performed independently of scale effects and boundary effects, and nowadays can include all the relevant physics, such as turbulence, free surface waves, internal waves and electromagnetic effects. Hence, carefully validated computer simulations of flows around ships and submarines can already match the best experimental measurements and have the additional advantage of containing information that in turn can be studied, post-processed and visualized at any time. We illustrate the development of modern computational methods by presenting results from flow studies that can be compared with experimentally measured data to give an illustration of the method´s capabilities and reliability. For these studies we have chosen the flow around a DARPA Suboff geometry and the flow past a modern surface combatant, the DTMB 5415 hull. These cases generally serve as benchmark cases for model development. Very good agreement is obtained with measured quantities, and it is clear that these computational methods are suitable for examining signatures and other properties of naval vessel.