Sleep benefits memory consolidation. The reviewed studies indicate that this consolidating effect is not revealed under all circumstances but is linked to specific psychological conditions. Specifically, we discuss to what extent memory consolidation during sleep depends on the type of learning materials, type of learning and retrieval test, different features of sleep and the subject population. Post-learning sleep enhances consolidation of declarative, procedural and emotional memories. The enhancement is greater for weakly than strongly encoded associations and more consistent for explicitly than implicitly encoded memories. Memories associated with expected reward gain preferentially access to sleep-dependent consolidation. For declarative memories, sleep benefits are more consistently revealed with recall than recognition procedures at retrieval testing. Slow wave sleep (SWS) particularly enhances declarative memories whereas rapid eye movement (REM) sleep preferentially supports procedural and emotional memory aspects. Declarative memory profits already from rather short sleep periods (1-2 h). Procedural memory profits seem more dose-dependent on the amount of sleep following the day after learning. Children's sleep with high amounts of SWS distinctly enhances declarative memories whereas elderly and psychiatric patients with disturbed sleep show impaired sleep-associated consolidation often of declarative memories. Based on the constellation of psychological conditions identified we hypothesize that access to sleep-dependent consolidation requires memories to be encoded under control of prefrontal-hippocampal circuitry, with the same circuitry controlling subsequent consolidation during sleep.