For a database hosted on Azure, i can view the recent history of the queries performed on it. This is through the Azure portal > Database > Manage > Administration > Que
Windows Azure SQL Database offers dynamic management views (DMVs) that return server state information that can be used to monitor the health of a server instance, diagnose problems, and tune performance.
For a list of available views refer to System Views (Windows Azure SQL Database).
For examples of how to find CPU-intensive queries, long-running queries and I/O intensive queries refer to Tuning SQL Azure Databases, Part 2.
For additional troubleshooting tips refer to Troubleshoot and Optimize Queries with Windows Azure SQL Database, Improving Your I/O Performance, Gaining Performance Insight into Windows Azure SQL Database, Troubleshooting Windows Azure SQL Database, Finding Blocking Queries in SQL Azure, March Madness – SQL Azure – sys.dm_exec_query_stats.
Also consider profiling at the application level, for instance as explained in Profiling Database Activity in the Entity Framework and Query Profiling SQL Azure when using Entity Framework or Linq-to-SQL.
For advanced monitoring consider deploying Windows Azure SQL Database Management Pack for System Center 2012.