Although there has been several progress on finite-dimensional representations of quantum affine superalgebras, most of key results in non-super theory are still missing. This talk aims to demonstrate difficulties and peculiarities arising in super theory. For this, we first review what is known (and not known) about finite-dimensional representations of quantum affine superalgebras of type A, mainly in terms of Drinfeld presentation and from purely representation-theoretic point of view. Then we discuss some super phenomena and hence which kind of statements can be expected for super, including the theory of q-characters.