Microcavity exciton-polaritons are hybrid quantum quasi-particles as an admixture of cavity photons and quantum-well excitons. The inherent light-matter duality provides experimental advantages to form coherent condensates at high temperatures (e.g. 4 K in GaAs and room temperature in GaN materials) and to access the dynamics of exciton-polaritons. At first I will present fundamental mathematical description of strongly coupled exciton-polaritons with the beauty of dynamical exciton-polariton condensates. We engineer exciton polariton-lattice systems, where we seek the beauty of non-zero momentum boson order arising from the intrinsic open-dissipative nature of the condensate as well as the topology of lattices. I will share our recent work on quantifying the hopping integrals of Bloch exciton-polaritons in a honeycomb lattice by varying two control physical parameters. I envision that the polariton- lattice systems will be an intellectual interface, where we may address wondrous quantum many-body problems in the light-matter domain.