Sleep has been found to have a beneficial effect on memory consolidation. It has furthermore frequently been suggested that sleep does not strengthen all memories equally. The first aim of this review paper was to examine whether sleep selectively strengthens emotional declarative memories more than neutral ones. We examined this first by reviewing the literature focusing on sleep/wake contrasts, and then the literature on whether any specific factors during sleep preferentially benefit emotional memories, with a special focus on the often-suggested claim that rapid eye movement sleep primarily consolidates emotional memories. A second aim was to examine if sleep preferentially benefits memories based on other cues of future relevance such as reward, test-expectancy or different instructions during encoding. Once again, we first focused on studies comparing sleep and wake groups, and then on studies examining the contributions of specific factors during sleep (for each future relevance paradigm, respectively). The review revealed that although some support exists that sleep is more beneficial for certain kinds of memories based on emotion or other cues of future relevance, the majority of studies does not support such an effect. Regarding specific factors during sleep, our review revealed that no sleep variable has reliably been found to be specifically associated with the consolidation of certain kinds of memories over others based on emotion or other cues of future relevance.