Wireless systems are an integral part of aviation. Apart from their apparent use in air-to-ground communication, wireless systems play a crucial role in avionic functions including navigation and landing. An interference-free wireless environment is therefore critical for the uninterrupted operation and safety of an aircraft. Hence, there is an urgency for airport facilities to acquire the capability to continuously monitor aviation frequency bands for real-time detection of interference and anomalies. To meet this critical need, we design and build AviSense, an SDR-based real-time, versatile system for monitoring aviation bands. AviSense detects and characterizes signal activities to enable practical and effective anomaly detection. We identify and tackle the challenges posed by a diverse set of critical aviation bands and technologies. We evaluate our methodology with real-world aviation signal measurements and two custom datasets of anomalous signals. We find that our signal classification capability achieves a true positive rate of ∼99%, with few exceptions, and a false positive rate of less than 4%. We also demonstrate that AviSense can effectively distinguish between different types of anomalies. We build and evaluate a prototype implementation of AviSense that supports distributed monitoring.