The US and UK (in contradiction to the EU) provide military support to the Saudi government and its coalition partners in their military action in Yemen. The US provides intelligence information and air tanker refueling for the Saudi Royal Airforce. The UK government sold $4.2 billion dollars with of military equipment and armaments to the Saudi government in 2015.
The US recognizes the current President of Yemen (Hadi) and his government as the legitimate government of Yemen. The Saudi-led Arab Coalition is in support of the Hadi government (Operation Decisive Storm) retaking full control of the country. The military action is against the Houthi militia, which captured the capital last year, and is allegedly supported/funded by Iran.
Many see this as a proxy war for regional influence between Saudi Arabia and Iran.
Here is a summary article (which my media site published) relating to US/UK involvement in Yemen: