Use of IQueryable and IEnumerable interfaces

IEnumerable<T> is applicable for in-memory data querying, in contrast IQueryable<T> allows remote execution, like web service or database querying. 

First of all, IQueryable<T> extends the IEnumerable<T> interface, so anything you can do with a "plain" IEnumerable<T>, you can also do with an IQueryable<T>.

Misuse of the interface can result in performance and memory problems, e.g. if IEnumerable<T> is used instead of IQueryable<T> to perform paging all the rows from data source will be loaded, instead of only those rows from the current page

IEnumerable<T> just has a GetEnumerator() method that returns an Enumerator<T> for which you can call its MoveNext() method to iterate through a sequence of T.

What IQueryable<T> has that IEnumerable<T> doesn't are two properties in particular—one that points to a query provider (e.g., a LINQ to SQL provider) and another one pointing to a query expressionrepresenting the IQueryable<T> object as a runtime-traversable expression that can be understood by the given query provider (for the most part, you can't give a LINQ to SQL expression to a LINQ to Entities provider without an exception being thrown).

The expression can simply be a constant expression of the object itself or a more complex tree of a composed set of query operators and operands. The query provider's IQueryProvider.Execute() orIQueryProvider.CreateQuery() methods are called with an Expression passed to it, and then either a query result or another IQueryable is returned, respectively.