In this paper, we consider possible solutions for noncoherent decoding of concatenated codes with spectrally efficient modulations. Two main classes of schemes are considered. A first class is obtained by concatenating parallel coding schemes with differential encoding. A second class considers serially concatenated coding structures and possible schemes derived from turbo trellis coded modulation (T-TCM), which do not employ differential encoding. In the first case, at the receiver side we consider separate detection and decoding, while in the second case we consider joint detection and decoding. The major problem connected with such an iterative decoding procedure is that taking into account an augmented channel memo~ leads to an intolerable trellis size, and hence to an impractical decoding complexity. Reduced-complexity techniques suited to iterative decoding become fundamental, and we consider a recently proposed state-reduction technique. This way, the performance of a coherent receiver is approached, by keeping the number of receiver states fixed.