Spiking neural network (SNN), widely known as the third-generation neural network, has been frequently investigated due to its excellent spatiotemporal information processing capability, high biological plausibility, and low energy consumption characteristics. Analogous to the working mechanism of human brain, the SNN system transmits information through the spiking action of neurons. Therefore, artificial neurons are critical building blocks for constructing SNN in hardware. Memristors are drawing growing attention due to low consumption, high speed, and nonlinearity characteristics, which are recently introduced to mimic the functions of biological neurons. Researchers have proposed multifarious memristive materials including organic materials, inorganic materials, or even two-dimensional materials. Taking advantage of the unique electrical behavior of these materials, several neuron models are successfully implemented, such as Hodgkin–Huxley model, leaky integrate-and-fire model and integrate-and-fire model. In this review, the recent reports of artificial neurons based on memristive devices are discussed. In addition, we highlight the models and applications through combining artificial neuronal devices with sensors or other electronic devices. Finally, the future challenges and outlooks of memristor-based artificial neurons are discussed, and the development of hardware implementation of brain-like intelligence system based on SNN is also prospected.