  We prove the dp-finite case of the Shelah conjecture on NIP fields. If K is a
dp-finite field, then K admits a non-trivial definable henselian valuation
ring, unless K is finite, real closed, or algebraically closed. As a
consequence, the conjectural classification of dp-finite fields holds.
Additionally, dp-finite valued fields are henselian. Lastly, if K is an
unstable dp-finite expansion of a field, then K admits a unique definable
V-topology.
