May 31st
1223 - Mongol invasion of the Cumans: Battle of the Kalka River - Mongol armies of Genghis Khan lead by Subutai defeat Kievan Rus and Cumans.
1862 - American Civil War Peninsula Campaign: Battle of Seven Pines or (Battle of Fair Oaks) - Confederate forces under Joseph E. Johnston & G. W. Smith engage Union forces under George B. McClellan outside Richmond, Virginia.
1864 - American Civil War Overland Campaign: Battle of Cold Harbor - The Army of Northern Virginia under Robert E. Lee engages the Army of the Potomac under Ulysses S. Grant & George G. Meade.
1916 - World War I: Battle of Jutland - The British Grand Fleet under the command of Sir John Jellicoe & Sir David Beatty engage the Kaiserliche Marine under the command of Reinhard Scheer & Franz von Hipper in the largest naval battle of the war, which proves indecisive.
Not much really