Perovskite materials have driven tremendous advances in constructing electronic devices owing to their low cost, facile synthesis, outstanding electric and optoelectronic properties, flexible dimensionality engineering, and so on. Particularly, emerging nonvolatile memory devices (eNVMs) based on perovskites give birth to numerous traditional paradigm terminators in the fields of storage and computation. Despite significant exploration efforts being devoted to perovskite-based high-density storage and neuromorphic electronic devices, research studies on materials' dimensionality that has dominant effects on perovskite electronics' performances are paid little attention; therefore, a review from the point of view of structural morphologies of perovskites is essential for constructing perovskite-based devices. Here, recent advances of perovskite-based eNVMs (memristors and field-effect-transistors) are reviewed in terms of the dimensionality of perovskite materials and their potentialities in storage or neuromorphic computing. The corresponding material preparation methods, device structures, working mechanisms, and unique features are showcased and evaluated in detail. Furthermore, a broad spectrum of advanced technologies (e.g., hardware-based neural networks, in-sensor computing, logic operation, physical unclonable functions, and true random number generator), which are successfully achieved for perovskite-based electronics, are investigated. It is obvious that this review will provide benchmarks for designing high-quality perovskite-based electronics for application in storage, neuromorphic computing, artificial intelligence, information security, etc.