Tiny waves driven by wind, shallow, long waves, head overlapping sea, all of these waves occur in every ocean and even in small lakes. The surface of water is one of the most versatile phenomenas of nature. Not only the movement of waves, but also the reflection of sky, sun and coastline makes the surface of water unique. Exactly this complexity is what brings its own challenges to the simulation of water surfaces. That is why simulation of water occupies mathematicians with a challenge for nearly 400 years now. In the last fifty years this challenge has more and more shifted to computer science. Computer graphic designers have tried to visualise water in a realistic manner for centuries. Science in this field expends from simple noise filters to mathematically complex solutions like Fourier Transformation. In the following work historical background of todays wave theories, as well as mathematical fundamentals are given. The focus of this work is set on the implementation of these methods in OpenGL 3.3.