Last.fm, a music discovery website, utilizes Hadoop infrastructure to manage and process large volumes of user interaction data, generating over 40 billion scrobbles and millions of streaming hours monthly. Their system comprises 44 nodes with specific hardware and software configurations, employing various tools like Hive and Dumbo for data analysis and processing. Use cases include site statistics, recommendations, and real-time user metrics, highlighting the significance of Hadoop in handling extensive data operations.