Over on YouTube icholakov has uploaded an informative video that gives an overview of the main communication modes that aircraft use from HF to UHF. In the video he also gives examples of those modes being received and decoded with an SDR.
The modes that he explains and demonstrates are VHF voice, VHF ATIS automated weather, ACARS short data messages, HF voice, HF automatic weather, HF data selective calling (SELCAL), HF data link (HFDL) and UHF ADS-B aircraft positioning.
Monitoring airplane communications
Over on YouTube Fuzz The Pi Guy has uploaded a video tutorial showing how to set up a Broadcastify air traffic control audio feed with RTL-Airband and an RTL-SDR running on a Raspberry Pi. This allows you to publicly share your received air traffic control audio online via sites like Broadcastify.
The video is based on a comprehensive Radioreference text tutorial which takes you through the process from scratch. Setting it up involves installing the Raspbian OS, installing RTL-SDR, installing and setting up RTL-Airband, configuring ezstream and then ensuring that everything runs automatically on boot. It's a fairly involved setup process, but the video helps make things easier.
How To Setup Broadcastify On A Raspberry Pi Using RTL_AM For Aviation