This book will describe recent theoretical advances of cold atom physics in optical lattices, concentrating on strongly correlated systems and possible applications in quantum information processing. Furthermore, the latest experiments aiming towards realizing these theoretical ideas will be discussed. The book will present in detail recently developed quantum optical tools for manipulating atoms in optical lattices and show how they can be used to realize a large range of well controlled many body Hamiltonians. Connections and differences to standard condensed matter physics will be explained. Finally, it will discuss how the ability to dynamically change parameters in these Hamiltonians on time scales much shorter than typical decoherence times can be exploited to realize quantum information processing devices with neutral atoms in optical lattices.