What's the difference between deque and list STL containers?

Let me list down the differences:

• Deque manages its elements with a dynamic array, provides random access, and has almost the same interface as a vector.
• List manages its elements as a doubly linked list and does not provide random access.

• Deque provides Fast insertions and deletions at both the end and the beginning. Inserting and deleting elements in the middle is relatively slow because all elements up to either of both ends may be moved to make room or to fill a gap.
• In List, inserting and removing elements is fast at each position, including both ends.

• Deque: Any insertion or deletion of elements other than at the beginning or end invalidates all pointers, references, and iterators that refer to elements of the deque.
• List: Inserting and deleting elements does not invalidate pointers, references, and iterators to other elements.

Complexity

             Insert/erase at the beginning       in middle        at the end

Deque:       Amortized constant                  Linear           Amortized constant
List:        Constant                            Constant         Constant

From the (dated but still very useful) SGI STL summary of deque:

A deque is very much like a vector: like vector, it is a sequence that supports random access to elements, constant time insertion and removal of elements at the end of the sequence, and linear time insertion and removal of elements in the middle.

The main way in which deque differs from vector is that deque also supports constant time insertion and removal of elements at the beginning of the sequence. Additionally, deque does not have any member functions analogous to vector's capacity() and reserve(), and does not provide any of the guarantees on iterator validity that are associated with those member functions.

Here's the summary on list from the same site:

A list is a doubly linked list. That is, it is a Sequence that supports both forward and backward traversal, and (amortized) constant time insertion and removal of elements at the beginning or the end, or in the middle. Lists have the important property that insertion and splicing do not invalidate iterators to list elements, and that even removal invalidates only the iterators that point to the elements that are removed. The ordering of iterators may be changed (that is, list::iterator might have a different predecessor or successor after a list operation than it did before), but the iterators themselves will not be invalidated or made to point to different elements unless that invalidation or mutation is explicit.

In summary the containers may have shared routines but the time guarantees for those routines differ from container to container. This is very important when considering which of these containers to use for a task: taking into account how the container will be most frequently used (e.g., more for searching than for insertion/deletion) goes a long way in directing you to the right container.

std::list is basically a doubly linked list.

std::deque, on the other hand, is implemented more like std::vector. It has constant access time by index, as well as insertion and removal at the beginning and end, which provides dramatically different performance characteristics than a list.

Another important guarantee is the way each different container stores its data in memory:

• A vector is a single contiguous memory block.
• A deque is a set of linked memory blocks, where more than one element is stored in each memory block.
• A list is a set of elements dispersed in memory, i.e.: only one element is stored per memory "block".

Note that the deque was designed to try to balance the advantages of both vector and list without their respective drawbacks. It is a specially interesting container in memory limited platforms, for example, microcontrollers.

The memory storage strategy is often overlooked, however, it is frequently one of the most important reasons to select the most suitable container for a certain application.

No. A deque only supports O(1) insertion and deletion at the front and back. It may, for example, be implemented in a vector with wrap-around. Since it also guarantees O(1) random access, you can be sure it's not using (just) a doubly linked list.