Memristive devices present a new device technology allowing for the realization of compact non-volatile memories. Some of them are already in the process of industrialization. Additionally, they exhibit complex multilevel and plastic behaviors, which make them good candidates for the implementation of artificial synapses in neuromorphic engineering. However, memristive effects rely on diverse physical mechanisms, and their plastic behaviors differ strongly from one technology to another. Here, we present measurements performed on different memristive devices and the opportunities that they provide. We show that they can be used to implement different learning rules whose properties emerge directly from device physics: real time or accelerated operation, deterministic or stochastic behavior, long term or short term plasticity. We then discuss how such devices might be integrated into a complete architecture. These results highlight that there is no unique way to exploit memristive devices in neuromorphic systems. Understanding and embracing device physics is the key for their optimal use.