  In this paper, we explain the connection between the Elephant Random Walk
(ERW) and an urn model \`a la P\'olya and derive functional limit theorems for
the former. The ERW model was introduced by Sch\"utz and Trimper [2004] to
study memory effects in a one-dimensional discrete-time random walk with a
complete memory of its past. The influence of the memory is measured in terms
of a parameter $p$ between zero and one. In the past years, a considerable
effort has been undertaken to understand the large-scale behavior of the ERW,
depending on the choice of $p$. Here, we use known results on urns to
explicitly solve the ERW in all memory regimes. The method works as well for
ERWs in higher dimensions and is widely applicable to related models.
