In the first part of the talk, I will discuss some recent work
on string theory on the background AdS3xS3xS3xS1. After a review of the
large N=4 superconformal symmetry the background supports, I will
discuss the BPS spectrum from a string theory and supergravity point of
view. I will make an explicit proposal for the dual CFT in the case
where the two D5-brane charges are multiples of each other, the matching
BPS spectrum will give convincing evidence in favour of this proposal.
In the second part of the talk, I will present some new explicit
examples of N=(2,2) dualities, which are obtained by orbifolding the
familiar dualities of AdS3xS3xT4 and the symmetric orbifold of T4. I
will explain various subtleties and checks of the proposal.