We start by reviewing UV completion of the Gross-Neveu model in dimensions between two and four via the Gross-Neveu-Yukawa model, which is a multi-flavor Yukawa theory. We discuss the operator scaling dimensions and the sphere free energy for these Conformal Field Theories. The case of a single two-component Majorana fermion is special in that the theory appears to flow to a CFT with emergent supersymmetry, and we provide evidence for this using 4-epsilon expansions. We also discuss the O(N) symmetric scalar theory in dimensions between four and six, where it appears to be unitary to all orders in the 1/N expansion, and propose its UV completion in terms of a cubic theory. In 6-epsilon dimensions this O(N) symmetric cubic theory has an IR stable fixed point for N>1038. We conclude with comments on continuation of this theory to five dimensions.