A traditional database systems is organized around a single data model that determines how data can be organized, stored and manipulated. But the vision of this paper is to develop new principles and techniques to manage multiple data models against a single, integrated backend. For example, semi-structured, graph and relational models are examples of data models that may be supported by a new system. Having a single data platform for managing both well-structured data and NoSQL data is beneficial to users; this approach significantly reduces integration, migration, development, maintenance and operational issues. The problem is challenging: the existing database principles mainly work for a single model and the research on multi-model data management is still at an early stage. In this paper, we envision a UDBMS (Unified Database Management System) for multi-model data management in one platform. UDBMS will provide several new features such as unified data model and flexible schema, unified query processing, unified index structure and cross-model transaction guarantees. We discuss our vision as well as present multiple research challenges that we need to address.