In production environments with large databases and high concurrent access, it might happen that queries that used to run in tens of milliseconds suddenly take several seconds.
Likewise, a summary query for a report that used to run in a few seconds might take half an hour to complete.
Here are some ways to find out what is slowing them down.
Any questions of the type "why is this different today from what it was last week?" are much easier to answer if you have some kind of historical data collection setup.
Tools such as Cacti or Munin (for monitoring general server characteristics such as CPU and RAM usage, disk I/O, network traffic, and load average) are very useful to see what has changed recently, ...