In the Standard Model, electroweak symmetry breaking is a crossover. In many extensions, the phase transition can be of first order – even strongly so. The resulting phase transition can then be a substantial source of gravitational waves. For a phase transition at or around the electroweak scale, these gravitational waves may be detectable by future or planned missions, such as LISA. This can indirectly provide a probe of particle physics beyond the Standard Model, complementary to future colliders. In this talk I will discuss the physics that will make this possible and present some new simulation results for strong phase transitions, showing that vorticity is generated during the phase transition and substantial reheating can occur in front of the bubbles. This slows them down and, in certain cases, can suppress the generation of gravitational waves from the phase transition.