I will give an introduction to random lattice triangulations. These are triangulations of the integer points inside the square [0,n] x [0,n] where each triangulation T is obtained with probability proportional to \lambda^|T|, where \lambda is a positive real parameter and |T| is the total length of the edges in T. I will discuss structural and dynamical properties of such triangulations, such as phase transitions with respect to \lambda, decay of correlations, local limits, and mixing time of Glauber dynamics. This is based on joint works with Pietro Caputo, Fabio Martinelli and Alistair Sinclair.