We will consider the possible structure of the Mitchell order on the set of κ-complete normal ultrafilters on a measurable cardinal κ. We outline two forcing methods for realizing various well founded orders of cardinality ≤ κ as the Mitchell order at κ:

1. The first method is used to realize a wide family of well founded orders called tame orders, and requires large cardinal assumptions weaker than o(κ)=κ⁺.
2. The second method assumes a large cardinal property slightly stronger than a sharp to a strong cardinal, and is used to realize every well founded order as the Mitchell order.