Power BI development supports three data connectivity modes: Import, DirectQuery, and Live Connection. Import mode loads data into Power BI, providing fast performance and offline capabilities but requiring periodic refreshes. DirectQuery allows real-time querying of data sources without importing, useful for large datasets, but may impact performance. Live Connection is used for connecting directly to Analysis Services, giving real-time data access with the same limitations as DirectQuery. Choosing the right mode depends on the balance between performance and real-time access requirements.