Memristive devices are highly promising candidates for overcoming the limits of conventional nonvolatile memory, such as flash memory, due to their high scalability, low power consumption, and simple structure. Moreover, memristive devices might be employed as hardware representations of synapses in neuromorphic circuits. Heterostructures of the perovskite Pr_1-xCa_xMnO₃ (PCMO) and a tunnel oxide are a well-studied system and a famous representative of area-dependent switching in the family of valence change memory. In contrast to filamentary switching, area-dependent switching can be tuned gradually, making it highly interesting for application in neuromorphic circuits. Further, PCMO-based devices are considered a persistent memory for DRAM replacement. This review discusses PCMO as a material and its properties, the types and aspects of memristive heterostructures based on PCMO, and different switching mechanisms. Finally, it provides an overview of the use of PCMO-based devices in neuromorphic applications and industrial activities on PCMO-based devices for memory.