Fragments of former oceans are commonly observed in mountain belts: blueschists and eclogites, on the one hand, and ophiolites, on the other hand, are all that remains of ancient oceanic lithosphere. Though volumetrically subordinate, they provide essential insights into past geodynamics and into the processes involved in the formation and destruction of oceanic lithosphere. This contribution apprehends these two types of oceanic fragments jointly and shows the advantage of doing so for understanding the dynamics of oceanic convergence, i.e. subduction and obduction. We examine the intimate relationships between blueschists/eclogites and ophiolites, as well as the similarities and differences in the mechanisms leading to their preservation. While the extensive, unmetamorphosed true ophiolites markedly differ from fragments of oceanic lithosphere offscraped from the slab during subduction, at shallow or great depths, both types record the mechanical behavior and 'hiccups' of the subduction plate boundary. Their preservation also highlights the importance of the evolution of the subduction regime through time, from the onset of intra-oceanic subduction to the cessation of continental subduction.