Gluing opposite sides of a parallelogram together gives a torus. A translation surface is a surface obtained by identifying sides of more complicated polygons by translations. They arise naturally when exploring both billiards trajectories and geodesics in the moduli space of curves. I will give an introduction to these objects and explain these connections. I will then present an important system of coordinates on the space parameterising translation surfaces, the period coordinates, and discuss results characterising the periods that can arise.