I will discuss recent progress in the theory of solitary water waves with weak surface tension. In the two-dimensional case there are solitary waves which asymptotically look like a wave packet governed by the nonlinear Schrödinger equation. I will discuss three-dimensional analogues of these solutions, which are either fully localised, that is localised in all horizontal directions, or localised in one direction and periodic in the orthogonal direction. These solutions can also be described as wave packets, where the amplitude equation is the Davey-Stewartson system. They are constructed using variational methods and dynamical systems theory. I will also discuss a connection to transverse instability of the two-dimensional solitary waves mentioned above.