In this talk, I will describe the axiomatic definition of a conformal superalgebra introduced by V. G. Kac and its generalization, a differential conformal superalgebra, due to V. G. Kac, M. Lau, and A. Pianzola. This generalization leads to the definition of twisted forms of conformal superalgebras, which can be classified using certain Hˆ1. Finally, I will state our recent results about the automorphism groups and twisted loop conformal superalgebras of the N=1,2,3, small N=4 and large N=4 conformal superalgebras.