An event-triggered mechanism is of great efficiency in reducing unnecessary sensor samplings/transmissions and, thus, resource consumption such as sensor power and network bandwidth, which makes distributed event-triggered estimation a promising resource-aware solution for sensor network-based monitoring systems. This paper provides a survey of recent advances in distributed event-triggered estimation for dynamical systems operating over resource-constrained sensor networks. Local estimates of an unavailable state signal are calculated in a distributed and collaborative fashion based on only invoked sensor data. First, several fundamental issues associated with the design of distributed estimators are discussed in detail, such as estimator structures, communication constraints, and design methods. Second, an emphasis is laid on recent developments of distributed event-triggered estimation that has received considerable attention in the past few years. Then, the principle of an event-triggered mechanism is outlined and recent results in this subject are sorted out in accordance with different event-triggering conditions. Third, applications of distributed event-triggered estimation in practical sensor network-based monitoring systems including distributed grid-connected generation systems and target tracking systems are provided. Finally, several challenging issues worthy of further research are envisioned.