January 31: Independence Day in Nauru (1968)
- 1578 – Eighty Years' War: Spain won a crushing victory in the Battle of Gembloux, hastening the disintegration of the unity of the rebel provinces and bringing an end to the Union of Brussels.
- 1801 – John Marshall became the fourth Chief Justice of the United States; his court opinions helped lay the basis for American constitutional law and made the Supreme Court a coequal branch of government.
- 1900 – Datu Muhammad Salleh, leader of a series of major disturbances in North Borneo, was shot dead in Tambunan, but his followers did not give up for five more years.
- 1942 – Second World War: Allied forces retreated from British Malaya to Singapore, ceding control of the country to Japan.
- 1996 – Japanese amateur astronomer Yuji Hyakutake discovered Comet Hyakutake (pictured), which was one of the closest cometary approaches of the previous 200 years.
- More anniversaries:
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