The success of cloud computing as a platform for deploying web-applications has led to a deluge of applications characterized by small data footprints but unpredictable access patterns. An autonomic and scalable multitenant database management system (DBMS) is therefore an important component of the software stack for platforms supporting these applications. Elastic load balancing is a key requirement for effective resource utilization and operational cost minimization. Efficient techniques for database migration are thus essential for elasticity in a multitenant DBMS. Our vision is a DBMS where multitenancy is viewed as virtualization in the database layer, and migration is a first class notion with the same stature as scalability, availability etc. This paper serves as the first step in this direction. We analyze the various models of database multitenancy, formalize the forms of migration, evaluate the off-the-shelf migration techniques, and identify the design space and research goals for an autonomic and elastic multitenant database.