Novel computing architectures based on resistive switching memories (also known as memristors or RRAMs) have been shown to be promising approaches for tackling the energy inefficiency of deep learning and spiking neural networks. However, resistive switch technology is immature and suffers from numerous imperfections, which are often considered limitations on implementations of artificial neural networks. Nevertheless, a reasonable amount of variability can be harnessed to implement efficient probabilistic or approximate computing. This approach turns out to improve robustness, decrease overfitting and reduce energy consumption for specific applications, such as Bayesian and spiking neural networks. Thus, certain non-idealities could become opportunities if we adapt machine learning methods to the intrinsic characteristics of resistive switching memories. In this short review, we introduce some key considerations for circuit design and the most common non-idealities. We illustrate the possible benefits of stochasticity and compression with examples of well-established software methods. We then present an overview of recent neural network implementations that exploit the imperfections of resistive switching memory, and discuss the potential and limitations of these approaches.