|Covid-19|January 6–January 13 – In the Eastern Hungarian Kingdom the Diet of Torda declares religious freedom firstly in Europe.
February 17 – Treaty of Adrianople (sometimes called the Peace of Adrianople): The Habsburgs agree to pay tribute to the Ottomans.
March 23 – The Peace of Longjumeau ends the Second War of Religion in France. Again Catherine de' Medici and Charles IX make substantial concessions to the Huguenots.
May 2 – Mary, Queen of Scots, escapes from Loch Leven Castle.
May 13 – Battle of Langside: The forces of Mary, Queen of Scots, are defeated by a confederacy of Scottish Protestants under James Stewart, Earl of Moray, her half-brother.
May 16 – Mary, Queen of Scots, flees to England.
May 19 – Queen Elizabeth I of England arrests Mary, Queen of Scots.
May 23 – Battle of Heiligerlee: Troops under Louis of Nassau, brother of William I of Orange, defeat a smaller loyalist force under the Duke of Arenberg in an attempt to invade the Northern Netherlands. This is effectively the start of the Eighty Years' War.
July 21 – Battle of Jemmingen: The main Spanish army of the Duke of Alva utterly defeats Louis of Nassau's invading army in the Northeastern Netherlands.
August 18 – The Third War of Religion begins in France after an unsuccessful attempt by the Royalists to capture Condé and Coligny, the Huguenot leaders.
September 23 – Battle of San Juan de Ulúa (Anglo-Spanish War): In the Gulf of Mexico, a Spanish fleet forces English privateers under John Hawkins to end their campaign.
September 29 – The Swedish king Eric XIV is deposed by his half-brothers John and Charles. John proclaims himself king John III the next day.
October 5 – William I of Orange invades the southeastern Netherlands.
October 20 – Battle of Jodoigne. Spanish forces under the Duke of Alva destroy Orange's rearguard. Orange abandons his offensive.
The Russo-Turkish War in Astrakhan begins.
Ashikaga Yoshiaki is installed as Shogun, beginning the Azuchi–Momoyama period in Japan.
Akbar the Great of the Mughal Empire besieges and captures the massive Chittorgarh Fort in northern India.
Polybius' "The Histories" first translated into English by Christopher Watson.
Huguenots besieged Chartres.
A Spanish expedition under Álvaro de Mendaña de Neira discovers the Solomon Islands
January 6 – Henri Spondanus, French historian (d. 1643)
January 14 – Johannes Hartmann, German chemist (d. 1631)
January 20 – Daniel Cramer, German theologian (d. 1637)
January 28 – Gustav of Sweden, Swedish prince (d. 1607)
January 30 – Katharina of Hanau-Lichtenberg, Countess (d. 1636)
February 2 – Péter Révay, Hungarian historian (d. 1622)
February 11 – Honoré d'Urfé, French writer (d. 1625)
March 9 – Aloysius Gonzaga, Italian Jesuit and saint (d. 1591)
March 16 – Juan Martínez Montañés, Spanish sculptor (d. 1649)
March 28 – Johannes Polyander, Dutch theologian (d. 1646)
April 5 – Pope Urban VIII (d. 1644)
April 17 – George Brooke, English aristocrat (d. 1603)
April 21 – Frederick II, Duke of Holstein-Gottorp (d. 1587)
April 28 – Teodósio II, Duke of Braganza, Portuguese nobleman and father of João IV of Portugal (d. 1630)
May 9 – Guglielmo Caccia, Italian painter (d. 1625)
May 11 – Christian I, Prince of Anhalt-Bernburg, German prince of the House of Ascania (d. 1630)
May 17 – Anna Vasa of Sweden, Swedish princess (d. 1625)
May 29 – Virginia de' Medici (d. 1615)
June 6 – Sophie of Brandenburg, Regent of Saxony (1591–1601) (d. 1622)
June 25 – Gunilla Bielke, Queen of Sweden (d. 1597)
July 1 – Philip Sigismund of Brunswick-Wolfenbüttel, Roman Catholic bishop (d. 1623)
August 27 – Hercule, Duke of Montbazon (d. 1654)
September 3 – Adriano Banchieri, Italian composer (d. 1634)
September 5 – Tommaso Campanella, Italian theologian and poet (d. 1639)
October 2 – Marino Ghetaldi, Croatian mathematician and physicist (d. 1626)
October 18 – Henry Wallop, English politician (d. 1642)
November 18 – Augustus the Elder, Duke of Brunswick-Lüneburg, Lutheran Bishop of Ratzeburg (d. 1636)
December 17 – Jonathan Trelawny, English politician (d. 1604)
Nikolaus Ager, French botanist (d. 1634)
John Welsh of Ayr, Scottish Presbyterian leader
Barnabe Barnes, English poet (d. 1609)
Edward Chichester, 1st Viscount Chichester (d. 1648)
Nakagawa Hidemasa, Japanese military leader (d. 1592)
Fernando de Alva Cortés Ixtlilxóchitl, Mexican historian (d. 1648)
Gervase Markham, English poet and writer (d. 1637)
Edward Somerset, 4th Earl of Worcester (d. 1628)
Henry Wotton, English author and diplomat (d. 1639)
Wei Zhongxian, Grand Secretary of China (d. 1627)
January 15 – Catherine Carey, Chief Lady of the Bedchamber to Elizabeth I of England (b. c. 1526)
January 20 – Myles Coverdale, English Bible translator (b. c. 1488)
January 21 – Amato Lusitano, Portuguese physician (b. 1511)
January 26 – Lady Catherine Grey, Countess of Hertford (b. 1539)
February 15 – Hendrick van Brederode, Dutch reformer (b. 1531)
March 20 – Albert, Duke of Prussia (b. 1490)
May 23 – Jean de Ligne, Duke of Arenberg (b. 1528)
June 3 – Andrés de Urdaneta, Spanish friar (b. 1498)
Lamoral, Count of Egmont, Flemish statesman (b. 1522)
Philip de Montmorency, Count of Horn (b. c. 1524)
July 7 – William Turner, British ornithologist and botanist (b. 1508)
July 24 – Carlos, Prince of Asturias, son of Philip II of Spain (b. 1545)
August 21 – Jean Parisot de Valette, 49th Grandmaster of the Knights Hospitaller (b. 1495)
August 23 – Thomas Wharton, 1st Baron Wharton (b. 1495)
September 22 – Jöran Persson, Swedish politician (b. c. 1530) (executed)
September 26 – Leonor de Cisneros, Spanish Protestant (b. 1536)
October 3 – Elisabeth of Valois, Queen of Philip II of Spain (b. 1545)
October 14 – Jacques Arcadelt, Flemish composer (b. 1504)
October 28 – Ashikaga Yoshihide, Japanese shogun (b. 1538)
November 6 – Herman of Kazan and Svyazhsk, archbishop of Kazan and later Metropolitan of Moscow
December 23 – Roger Ascham, tutor of Elizabeth I of England (b. 1515)
December 31 – Shimazu Tadayoshi, Japanese warlord (b. 1493)
Henry Sutton Dudley, English soldier and sailor (b. 1517)
Garcia de Orta, Portuguese Jewish physician (b. 1501)
Dirk Philips, early Anabaptist writer and theologian
Yan Song, Chinese prime minister (b. 1481)
Year 1568 (MDLXVIII) was a leap year starting on Thursday (link will display the full calendar) of the Julian calendar.