The software used to manage database systems is known as Database Management Systems (DBMS), which allows users to create, retrieve, update, and manage data. Common types of DBMS include relational, NoSQL, and object-oriented systems. Popular examples are MySQL, PostgreSQL, and MongoDB. DBMS provides an interface for users and applications to interact with the databases securely and efficiently while ensuring data integrity, backup, and recovery capabilities. They play a critical role in handling large amounts of data in various applications.