This book presents analytic and numerical studies of magnetism in strongly correlated solid-state systems. Competing tendencies in these systems can lead to spontaneous nanoscale structures, such as stripes and checkerboards. There are three topics explored in this book. First, spin waves and magnetic excitations for well-ordered spin structures are studied by using a suitably parametrized Heisenberg model. Both site-centered and bond-centered antiphase domain walls are considered for a range of spacings between stripes and checkerboard antiphase domain walls. Second, quasi-two-dimensional spin systems are explored by using the Stochastic Series Expansion Quantum Monte Carlo method. The order-disorder phase transitions are studied for both static and dynamic bond-diluted Heisenberg spin systems. Varying the interlayer coupling, the Neel temperature and universal scalings are studied for weakly coupled Heisenberg antiferromagnetic layers consisting of coupled ladders. Third, a two-dimensional Heisenberg antiferromagnet with nearest-neighbor and four-spin ring exchange is studied, which exhibits a quantum phase transition from the Valence Bond Solid phase to Neel order.