Graphical models are a statistical tool used for a wide range of applications. There has been a huge amount of research in this topic across statistics, mathematics and computer science in the last few decades, and the timing is right for a handbook that presents an overview of the state-of-the-art. This handbook presents a comprehensive overview of the area through a collection of 25-30 chapters from some of the leading researchers. Each chapter has been carefully edited to ensure that the handbook is consistent in style, level and notation, and that it is accessible for graduate students and researchers new to the topic. It is sure to become a landmark reference in the area.