Theory and experiments on pure PbTiO3 under pressure show that a morphotropic phase boundary (MPB) exists in pure PbTiO3 under pressure, and that the high coupling materials including PZT and PMN-PT simply tune this transition to room pressure chemically. Using this idea of chemical pressure, we are searching for new high coupling piezoelectrics. It would be useful to have strong coupling materials that (1) work to higher temperatures (have higher Tc or TR-T), (2) have higher coercive fields, and (3) are pure compounds that melt congruently. Two candidates we have been studying are (Pb,Sn)TiO3 and (Pb,Sn)ZrO3 We find these material to have an orthorhombic or monoclinic ground states, and a higher energy tetragonal phase with large c/a strain. The energy difference is very small, so that thepolarization can be easily rotated, which suggests very strong piezoelectric constants. Other new materials will also be discussed A key question is whether relaxor behavior in relaxor ferroelectricsis significant to the origin of high electromechanical coupling. Simulations show that the most probable cause for relaxor behavior in PMN-type relaxors is from polar nanoregions (PNR) that form in chemically ordered regions (COD), and that PNR form around COR. This suggests that the large coupling and presence of MPB are separate from the relaxor behavior. We have experimentally studied X-ray diffuse scattering in PSN as a function of pressure and temperature. Molecular dynamics with a first-principles based effective Hamiltonian gives theobserved anisotropic diffuse X-ray scattering, and the origin of the scattering will be discussed. Finally, new experiments on high-pressure ferroelectricity will be discussed.