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We have performed ab initio electronic structure calculations and Monte Carlo simulations of frustrated ferroic materials where complex magnetic configurations and chemical disorder lead to rich phase diagrams. With lowering of temperature, we find a ferromagnetic phase which transforms to an antiferromagnetic phase at the magnetostructural (martensitic) phase transition and to a cluster spin glass at still lower temperatures. The Heusler alloys Ni-(Co)-Mn-(Cr)-(Ga, Al, In, Sn, Sb) are of particular interest because of their large inverse magnetocaloric effect associated with the magnetostructural transition and the influence of Co/Cr doping. Besides spin glass features, strain glass behavior has been observed in Ni-Co-Mn-In. The numerical simulations allow a complete characterization of the frustrated ferroic materials including the Fe-Rh-Pd alloys.