In recent years, spiking neural networks (SNNs) have received extensive attention in brain-inspired intelligence due to their rich spatially-temporal dynamics, various encoding methods, 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. This paper reviews recent advances and discusses new frontiers in SNNs from five major research topics, including essential elements (i.e., spiking neuron models, encoding methods, and topology structures), neuromorphic datasets, optimization algorithms, software, and hardware frameworks. We hope our survey can help researchers understand SNNs better and inspire new works to advance this field.