James Serra has a good post on moving your on-premise SQL Server instance up to Azure SQL Database:
In this migration process you migrate both your schema and your data from the SQL Server database in your current environment into SQL Database, provided the existing database passes compatibility tests. Fortunately with SQL Database Version 12 (V12), there are very few remaining compatibility issues other than server-level and cross-database operations (see Azure SQL Database Transact-SQL differences). Databases and applications that rely on partially or unsupported functions will need some re-engineering to fix these incompatibilities before the SQL Server database can be migrated.
Two years ago, I would have laughed at the idea. Right now, I’m skeptical. My expectation is that, two years from now, this will be my default answer for non-sensitive data.