I will summarise work done and in progress obtaining certain superblocks in various supersymmetric theories - in particular focussing on further explorations of new relations with the mathematical literature on symmetric polynomials and CMS systems uncovered recently by Isachenkov and Schomerus. Then focussing on N=4 SYM I will outline some recent applications of their use in bootstrapping quantum gravity on AdS space via AdS/CFT.