One of the filtered index use cases mentioned in the product documentation concerns a column that contains mostly NULL values. The idea is to create a filtered index that excludes the NULLs, resulting in a smaller nonclustered index that requires less maintenance than the equivalent unfiltered index.
Another popular use of filtered indexes is to filter NULLs from a UNIQUE index, giving the behaviour users of other database engines might expect from a default UNIQUE index or constraint: Uniqueness enforced only for non-NULL values.
Unfortunately, the query optimizer has limitations where filtered indexes are concerned. This post looks at a couple of less well-known examples.