The dynamics of ultracold bosonic atoms in an optical lattice can be described by a Bose-Hubbard model, where the system parameters are controlled by laser light. The authors study the continuous quantum phase transition from a superfluid to a Mott insulator phase as the depth of the optical potential is varied. In the Mott insulator phase, the atomic wave function becomes localized, and the density per site is pinned at integer values, forming an "optical crystal" with long-range order. The transition is predicted to occur at a critical ratio of the onsite interaction to the tunneling matrix element. The authors present numerical results and mean-field calculations to illustrate the formation of the Mott insulator phase in both homogeneous and inhomogeneous optical lattices, including the effects of additional harmonic traps and superlattices. They also discuss the role of collisions between atoms in the Mott phase and the experimental signatures of the Mott state, such as reduced density-density fluctuations and gapped particle-hole excitations. The ability to manipulate both the lattice and system parameters in this model opens new avenues for studying disordered Bose systems and the Bose glass phase.The dynamics of ultracold bosonic atoms in an optical lattice can be described by a Bose-Hubbard model, where the system parameters are controlled by laser light. The authors study the continuous quantum phase transition from a superfluid to a Mott insulator phase as the depth of the optical potential is varied. In the Mott insulator phase, the atomic wave function becomes localized, and the density per site is pinned at integer values, forming an "optical crystal" with long-range order. The transition is predicted to occur at a critical ratio of the onsite interaction to the tunneling matrix element. The authors present numerical results and mean-field calculations to illustrate the formation of the Mott insulator phase in both homogeneous and inhomogeneous optical lattices, including the effects of additional harmonic traps and superlattices. They also discuss the role of collisions between atoms in the Mott phase and the experimental signatures of the Mott state, such as reduced density-density fluctuations and gapped particle-hole excitations. The ability to manipulate both the lattice and system parameters in this model opens new avenues for studying disordered Bose systems and the Bose glass phase.