Advancement in mobile computing technologies has prompted strong needs for database systems that can be used in small devices such as sensors, cellular phones, PDAs, car navigators, and Ultra Mobile PCs (UMPCs). We term the database systems that are customizable for small computing devices as Ubiquitous Database Management Systems (UDBMSs). In this paper, we first review the requirements of the UDBMS. The requirements identified include lightweight DBMSs, selective convergence, flash-optimized storage systems, data synchronization, support of unstructured/semistructured data, complex database operations, selfmanagement, and security. Next, we review existing systems and research prototypes. We review the functionality of UDBMSs including the footprint size, support of standard SQL, transaction management, concurrency control, recovery, indexing, and access control. We then review the supportability of the requirements by those UDBMSs surveyed. We finally present research issues related to the UDBMS.