Gauge/gravity correspondence or dualities are useful nonperturbative methods for string theory and quantum gravity, and vice versa for strongly coupled quantum systems and quantum field theories. It manifests relation between quantum theory with gravity in higher dimensions and dual quantum system in lower dimensions. We discuss coherent state operators describing various giant gravitons, wrapped branes, and other excitations on spacetime. There are various emergent phenomena, including the emergence of the bulk spacetimes and excitations thereof. We construct also coherent states in the $SL(2)$ sectors and their cousin $PSU(1,1|2)$ sectors. The coherent state amplitudes are further packaged into supermatrix, which encode information of giants and dual giants. We add strings onto the coherent state operators. The string-added coherent states capture near-BPS states. The coherent state representations, auxiliary integrals, as well as auxiliary susy integrals, facilitate the computations efficiently. We generate correlation functions of integrated operators from correlation functions of un-integrated operators. Various other new techniques including new saddle point method, localization, analytic combinatorics, permutations are also briefly overviewed.