Real-time remote control over wireless is an important-yet-challenging application in 5G and beyond due to its mission-critical nature under limited communication resources. Current solutions hinge on not only utilizing ultra-reliable and low-latency communication (URLLC) links but also predicting future states, which may consume enormous communication resources and struggle with a short prediction time horizon. To fill this void, in this article we propose a novel two-way Koopman autoencoder (AE) approach wherein: 1) a sensing Koopman AE learns to understand the temporal state dynamics and predicts missing packets from a sensor to its remote controller; and 2) a controlling Koopman AE learns to understand the temporal action dynamics and predicts missing packets from the controller to an actuator co-located with the sensor. Specifically, each Koopman AE aims to learn the Koopman operator in the hidden layers while the encoder of the AE aims to project the non-linear dynamics onto a lifted subspace, which is reverted into the original non-linear dynamics by the decoder of the AE. The Koopman operator describes the linearized temporal dynamics, enabling long-term future prediction and coping with missing packets and closed-form optimal control in the lifted subspace. Simulation results corroborate that the proposed approach achieves a 38x lower mean squared control error at 0 dBm signal-to-noise ratio (SNR) than the non-predictive baseline.