In recent years, spiking neural networks (SNNs) have received extensive attention in the field of brain-inspired intelligence due to their rich spatially-temporal dynamics, various coding schemes, and event-driven characteristics that naturally fit the neuromorphic hardware. With the development of SNNs, brain-inspired intelligence, an emerging research field inspired by brain science achievements and aiming at artificial general intelligence, is becoming hot. In this paper, we review the recent advances and discuss the new frontiers in SNNs from four major research topics, including essential elements (i.e., spiking neuron models, encoding methods, and topology structures), datasets, optimization algorithms, and software and hardware frameworks. We hope our survey can help researchers understand SNNs better and inspire new works to advance this field.