Ultracold atomic gases in optical lattices can mimic condensed matter physics and beyond. These systems are nearly perfect realizations of various Hubbard models and can be used as quantum simulators to address open questions in condensed matter and high energy physics. The review discusses how these systems can be employed to study disordered, frustrated, spinor, and artificial magnetic field lattice gases, as well as quantum information processing. It covers the Hubbard and spin models, methods of treatment, and recent progress in cold atom systems. The review also addresses challenges such as Anderson localization, spin glasses, high Tc superconductivity, frustrated antiferromagnets, topological order, and quantum computing. It highlights the potential of ultracold gases to study strongly correlated systems, quantum spin liquids, and other exotic phases. The review emphasizes the role of optical lattices in creating controlled environments for studying quantum phenomena and their applications in quantum information and simulation.Ultracold atomic gases in optical lattices can mimic condensed matter physics and beyond. These systems are nearly perfect realizations of various Hubbard models and can be used as quantum simulators to address open questions in condensed matter and high energy physics. The review discusses how these systems can be employed to study disordered, frustrated, spinor, and artificial magnetic field lattice gases, as well as quantum information processing. It covers the Hubbard and spin models, methods of treatment, and recent progress in cold atom systems. The review also addresses challenges such as Anderson localization, spin glasses, high Tc superconductivity, frustrated antiferromagnets, topological order, and quantum computing. It highlights the potential of ultracold gases to study strongly correlated systems, quantum spin liquids, and other exotic phases. The review emphasizes the role of optical lattices in creating controlled environments for studying quantum phenomena and their applications in quantum information and simulation.