Master of Science / There has been an astronomical increase in data at the network edge due to the rapid development of 5G infrastructure and the proliferation of the Internet of Things (IoT). In order to improve the network controller's decision-making capabilities and improve the user experience, it is of paramount importance to properly analyze this data. However, transporting such a large amount of data from edge devices to the network controller requires large bandwidth and increased latency, presenting a significant challenge to resource-constrained wireless networks. By using information processing techniques, one could effectively address this problem by sending only pertinent and critical information to the network controller. Nevertheless, finding critical information from high-dimensional observation is not an easy task, especially when large amounts of background information are present. Our thesis proposes to extract critical but low-dimensional information from high-dimensional observations using an information-theoretic deep learning framework. We focus on two distinct problems where critical information extraction is imperative. In the first problem, we study the problem of feature extraction from video frames collected in a dynamic environment and showcase its effectiveness using a video game simulation experiment. In the second problem, we investigate the detection of anomaly signals in the spectrum by extracting and analyzing useful features from spectrograms. Using extensive simulation experiments based on a practical data set, we conclude that our proposed approach is highly effective in detecting anomaly signals in a wide range of signal-to-noise ratios.