While representation theory of quantum affine superalgebras is surprisingly unexplored, recent advances in both representation theory and related geometry and physics are shedding a new light, allowing us to overcome conceptual hurdles and pose a right question. In this talk, we will discuss such understandings and remaining problems by focusing on calculation of simple q-characters in the super type A. We first consider the category of polynomial modules governed by Schur-Weyl duality and super duality, which yields a Kazhdan-Lusztig type answer. Then we move on to a more general and practical algorithm à la Frenkel and Mukhin built on (2-parameter) deformed Cartan matrices.