In this chapter, we explain how to implement a simple, generic and efficient adaptive mesh refinement kernel on graphics processors. This kernel maps a refined connectivity onto coarse polygons in a single pass at vertex shading stage, enabling arbitrary displacement at high resolution in real-time. This book chapter summarizes the following research papers: "A Flexible Kernel for Adaptive Mesh Refinement on GPU" (CGF 2008), "Generic Mesh Refinement On GPU" (Graphics Hardware 2005). See also how we use this kernel for real-time approximation of subdivision surfaces (Pacific Graphics 2007). This kernel can also be used for rendering Scalar-Tagged PN Triangles (Eurographics 2005).