Summary: We consider output-feedback predictor-based stabilization of networked control systems with large unknown time-varying communication delays. For systems with two networks (sensors-to-controller and controller-to-actuators), we design a sampled-data observer that gives an estimate of the system state. This estimate is used in a predictor that partially compensates unknown network delays. We emphasize the purely sampled-data nature of the measurement delays in the observer dynamics. This allows an efficient analysis via the Wirtinger inequality, which is extended here to obtain exponential stability. To reduce the number of sent control signals, we incorporate the event-triggering mechanism. For systems with only a controller-to-actuators network, we take advantage of continuously available measurements by using a continuous-time predictor and employing a recently proposed switching approach to event-triggered control. For systems with only a sensors-to-controller network, we construct a continuous observer that better estimates the system state and increases the maximum output sampling, therefore, reducing the number of required measurements. A numerical example illustrates that the predictor-based control allows one to significantly increase the network-induced delays, whereas the event-triggering mechanism significantly reduces the network workload.