This talk introduces 2D synchrosqueezed transforms for image analysis with applications in geophysics and materials science. A synchrosqueezed transform consists of a phase-space transform with application dependent geometric scaling parameters, and a synchrosqueezing technique for a sharpened phase-space representation. In the case of a superposition of wave-like components with well-separated wave-vectors, it is proved that the synchrosqueezed transform is capable of recognizing each component and precisely estimating local wave-vectors. These properties make 2D synchrosqueezed transforms well suitable for 2D mode decomposition problems in geophysics and crystal image analysis in materials science.