The physics of strong correlations has at its core a competition between the delocalizing effects of the kinetic energy, and the localizing Coulomb potential. The classic competition is thus the Mott transition between paramagnetic metal and insulating antiferromagnet, but physical systems often add many complexities, via chemical doping, multiple orbitals, and coupling to the lattice degrees of freedom. Combined with this extra interplay, the result is quite frequently the appearance of various types of spatially modulated phases, with simple examples being charge- and spin-density waves, but most importantly new phases of coupled modulated order – where several broken symmetry states coexist in complex spatial patterns. This chapter views this topic via an examination of three different physical systems: the doped Mott insulator La2NiO4+δ; the magnetic and/or charge-ordered states of the doped manganites based on LaMnO3; and the heavy fermion superconductor CeCoIn5.