One of the main bottlenecks in the graphics pipeline nowadays is the memory bandwidth available between the CPU and the GPU. To avoid this bottleneck, programmable features were inserted into the video cards. With the Geometry Shader launch it is possible to create vertices in the GPU, however, this pipeline stage has a low performance. With the new graphic APIs (DirectX11 and OpenGL4) a Tessellator stage that allows massive vertex generation inside the GPU was created. This dissertation studies this new pipeline stage, as well as presents classic algorithms (PN-Triangles and Phong Tessellation) that were originally designed for CPU and proposes new algorithms (Tubes and Terrain rendering in the GPU) that takes advantage of this new paradigm.