Frustrated magnetism attracts much attention due to the competition between various magnetic states including the quantum spin liquid state, a disordered magnetic state with quantum entanglement. I will first discuss the physics of triangular lattice antiferromagnets with strong spin-orbit coupling based on recent and ongoing studies on KCeS2. Then I will introduce our project on the study of frustrated lattices of both electric and magnetic dipoles. Concretely we plan the single crystal growth and characterization by thermodynamic and microscopic measurements of the members of a family of such compounds: the hexaaluminates LnMgAl11O19 (Ce, Pr, Nd, Sm, Eu, Gd) and EuAl12O19 and hexagallates LnMgGa11O19 (Ce, Pr) and EuGa12O19. A particular attention will be given to the nature of the ground state of these compounds and to the coupling between the electric, magnetic and structural properties in these materials. This research is expected to lead to the discovery of new multiferroic phases and of new magnetoelectric glassy or quantum liquid phases.