January 1: The Public Order Act goes into effect in the United Kingdom, banning the wearing of political uniforms and empowering the police to stop political marches when there is risk of disorder.

January 1: Alan Turing's seminal 1936 paper on the principles of modern computing is published entitled On Computable Numbers, with an Application to the Entscheidungsproblem in which is presented the concept of a Universal Turing Machine.

January 5: Water levels begin to rise in the Ohio River in the United States, leading to the Ohio River flood of 1937, which continues into February, leaving 1 million people homeless and 385 people dead.

January 15: Spanish Civil War: Second Battle of the Corunna Road ends inconclusively.

January 19: Howard Hughes sets a new transcontinental aviation record by flying from Los Angeles to New York in 7 hours, 28 minutes and 25 seconds.

January 20: Second inauguration of Franklin D. Roosevelt: Franklin D. Roosevelt is sworn in for a second term as President of the United States. This is the first time that the United States presidential inauguration occurs on this date; the change is due to the ratification in 1933 of the Twentieth Amendment to the United States Constitution.

January 23: Moscow Trials: Trial of the Anti-Soviet Trotskyist Center In the Soviet Union 17 leading Communists go on trial, accused of participating in a plot led by Leon Trotsky to overthrow Joseph Stalin's regime, and assassinate its leaders (source: Wikipedia)