This book is provides an insight into the problem of optimal routing in geometric graphs. A geometric graph is a graph in which each node has location information, and edges have some geometrical constraints. The problems considered in this book fall into two main categories(1) routing in ad hoc wireless networks (2) routing through weighted regions. The fundamental problem in ad hoc wireless networks is broadcasting messages without flooding and it is modeled on unit disk graphs. The Weighted Region Problem deals with finding an optimal route between two points in the plane, and is modeled on a planar graph where paths are allowed to pass through the faces.