|Covid-19|March 13 – Battle of Tondibi: In Mali, forces sent by the Saadi Dynasty ruler of Morocco, Ahmad al-Mansur, and led by Judar Pasha, defeat the Songhai Empire, despite being outnumbered by at least five to one.
April 10 – English merchant James Lancaster sets off on a voyage to the East Indies.
April 21 – Japanese tea-master Sen no Rikyū commits seppuku on the order of Toyotomi Hideyoshi.
May 15 – In Russia, Tsarevich Dimitri, son of the Ivan the Terrible, is found dead in mysterious circumstances, at the palace in Uglich. The official explanation is that he has cut his own throat during an epileptic seizure. Many believe he has been murdered by his rival, Boris Godunov, who becomes tsar.
May 24 – Sir John Norreys, with an expeditionary force sent by Queen Elizabeth I of England, takes the town of Guingamp after a brief siege, on behalf of Henry of Navarre.
May 30 – Timbuktu is captured by an expedition of Arma people sent by the Saadi ruler of Morocco and led by Judar Pasha.
June – Zutphen is captured by the Dutch under Maurice of Nassau.
July – Deventer is captured by the Dutch under Maurice of Nassau.
July 22 – The Durtnell (Dartnell) family of Brasted, Kent, England, begin to work as building contractors. They will still be functioning under the twelfth generation of the family in the 21st century.
August – Robert Devereux, Earl of Essex leads an English army in support of the Protestant Henry IV of France at the Siege of Rouen.
Maurice maneuvers cautiously against the Duke of Parma near Arnhem.
During this year's Atlantic hurricane season, probably the most severe of the pre-1600 seasons, at least eight intense hurricanes occur.
September 1 – HMS Revenge is captured by the Spanish following battle near the Azores.
September 14 – Hulst is captured by Maurice.
October 21 – Nijmegen is captured by Maurice.
October 26 – Portuguese invasion of Jaffna kingdom opens.
October 29 – Pope Innocent IX succeeds Pope Gregory XIV as the 230th pope.
The city of Hyderabad, India is founded by Muhammad Quli Qutb Shah.
The Rialto Bridge in Venice, designed by Antonio da Ponte, is completed.
Publication of the first of the Conimbricenses commentaries on Aristotle by the Jesuits of the University of Coimbra.
January 3 – Valentin de Boulogne, Painter (d. 1632)
January 4 – William Spencer, 2nd Baron Spencer of Wormleighton, British Baron (d. 1636)
January 7 – Dorothea, Abbess of Quedlinburg, Princess (d. 1617)
January 11 – Robert Devereux, 3rd Earl of Essex, English Civil War general (d. 1646)
January 12 – Jusepe de Ribera, Spanish Tenebrist painter and printmaker (d. 1652)
January 15 – David van Goorle, theologian and theoretical scientist (d. 1612)
January 26 – Matthew Boynton, English politician (d. 1647)
January 29 – Franciscus Junius, the younger (d. 1677)
Hervey Bagot, English politician (d. 1660)
Guercino, Italian painter (d. 1666)
February 13 – Antonio Sabino, Italian composer (d. 1650)
February 21 (or March 2) – Girard Desargues, French mathematician (d. 1661)
February 25 – Friedrich von Spee, German Jesuit and poet (d. 1635)
February 28 – Henry Clifford, 5th Earl of Cumberland, English politician (d. 1643)
March 6 – Tommaso Tamburini, Italian theologian (d. 1675)
March 9 – Johannes Chrysostomus vander Sterre (d. 1652)
March 11 – Isabella of Savoy, Italian noble (d. 1626)
March 15 – Alexandre de Rhodes, French Jesuit missionary (d. 1660)
March 19 – Dirck Hals, Dutch painter (d. 1656)
March 28 – William Cecil, 2nd Earl of Salisbury, English earl (d. 1668)
April 5 – Frederick Ulrich, Duke of Brunswick-Lüneburg, Prince (d. 1634)
April 11 – Bartholomeus Strobel, Polish artist German painter (d. 1650)
April 25 – Marcos de Torres y Rueda (d. 1649)
May 2 – Francis Charles of Saxe-Lauenburg, Prince (d. 1660)
May 5 – Frederick Achilles, Duke of Württemberg-Neuenstadt (d. 1631)
May 26 – Olimpia Maidalchini, politically active Roman noble (d. 1657)
June 16 – Joseph Solomon Delmedigo, Italian physician, mathematician, and music theorist (d. 1655)
July 4 – Jonathan Rashleigh, English politician (d. 1675)
July 9 – Jean Bagot, French theologian (d. 1664)
July 20 – Anne Hutchinson, English Puritan preacher (d. 1643)
August 6 – George William, Count Palatine of Zweibrücken-Birkenfeld (d. 1654)
August 12 – Louise de Marillac, co-founder (d. 1660)
August 24 – Robert Herrick, English poet (d. 1674)
August 28 – John Christian of Brieg, Duke of Brzeg (1602–1639) (d. 1639)
September 8 – Marie Angélique Arnauld (d. 1661)
September 29 – Michael de Sanctis, Spanish saint (d. 1625)
October 2 – Margherita Gonzaga, Duchess of Lorraine (1608–1624) (d. 1632)
October 7 – Pierre Le Muet, French architect (d. 1669)
October 22 – Alfonso III d'Este, Duke of Modena, Italian noble (d. 1644)
November 20 – George Albert II, Margrave of Brandenburg (d. 1615)
November 29 – Bernhard von Mallinckrodt, German bibliophile (d. 1664)
December 22 – Tommaso Dingli, Maltese architect and sculptor (d. 1666)
December 30 – Joseph Furttenbach, German architect (d. 1667)
David Blondel, French Protestant clergyman (d. 1655)
Andrew Bobola, Polish Jesuit missionary and martyr (d. 1657)
Thomas Goffe, English dramatist (d. 1629)
William Lenthall, English politician of the Civil War period (d. 1662)
April 21 – Sen no Rikyu, Japanese exponent of the tea ceremony (b. 1522)
May 1 – Elizabeth Cecil, 16th Baroness de Ros, English Noblewoman (b. c. 1574)
May 15 – Tsarevich Dimitri, Tsarevich (b. 1582)
June 21 – Aloysius Gonzaga, Italian Jesuit and saint (b. 1568)
July 2 – Vincenzo Galilei, Italian composer (b. 1520)
July 18 – Jacobus Gallus Carniolus, Slovenian composer (b. 1550)
August 23 – Luis Ponce de León, Spanish lyric poet (b. 1527)
August 27 – Katheryn of Berain, Welsh noblewoman (b. 1534)
September 10 – Richard Grenville, English soldier and explorer (b. 1542)
October 16 – Pope Gregory XIV (b. 1535)
November 20 – Christopher Hatton, English politician (b. 1540)
December 14 – Saint John of the Cross, Spanish Carmelite friar and poet (b. 1542)
December 18 – Marigje Arriens, Dutch woman executed for witchcraft (b. c. 1520)
December 30 – Pope Innocent IX (b. 1519)
Crispin van den Broeck, Flemish painter (b. 1523)
John Erskine of Dun, Scottish religious reformer (b. 1509)
Toyotomi Hidenaga, Japanese nobleman (b. 1540)
John Stubbs, English pamphleteer (b. 1543)
Veronica Franco, Italian poet and courtesan (b. 1546)
1591 (MDXCI) was a common year starting on Tuesday (dominical letter F) of the Gregorian calendar and a common year starting on Friday (dominical letter C) of the Julian calendar, the 1591st year of the Common Era (CE) and Anno Domini (AD) designations, the 591st year of the 2nd millennium, the 91st year of the 16th century, and the 2nd year of the 1590s decade. As of the start of 1591, the Gregorian calendar was 10 days ahead of the Julian calendar, which remained in localized use until 1923.