In this paper, event-triggered estimators are designed for discrete-time recurrent neural networks (RNNs) with unknown time-delay. Owing to the diversity and complexity of time-delays, it is difficult to accurately predict their information. Under the boundedness of activation functions, the delay-depend term is regarded as a bounded nonlinear disturbance. Two event-triggered estimators are designed to estimate the neuron states. The first one considers the case that the system states are subject to unknown time-delay, and the second one deals with the case that both the system states and measurement outputs are subject to unknown time-delay. The sufficient conditions are developed to guarantee the input-to-state practical stability of estimation error systems. Finally, the dynamic event-triggered strategy is introduced to further reduce the events. Two numerical examples are given to show the validity of the developed scheme.