|Covid-19|January 16 – Charles I, having already abdicated as Holy Roman Emperor, resigns the Kingdom of Spain in favour of his son, Philip II, and retires to a monastery.
January 23 – The Shaanxi earthquake, the deadliest earthquake in history, occurs with its epicenter in Shaanxi province, China; 830,000 people may have been killed.
February 5 – Truce of Vaucelles: Fighting temporarily ends between France and Spain.
Akbar ascends to the throne of the Mughal Empire at age 13; he will rule until his death in 1605 by which time most of the north and centre of the Indian subcontinent will be under his control.
Archbishop of Canterbury Thomas Cranmer is declared a heretic.
February 22 (approx.) – Sophia Jagiellon marries Henry V, Duke of Brunswick-Lüneburg.
March 21 – In Oxford, Thomas Cranmer is burned at the stake for treason.
November – The Truce of Vaucelles collapses, and war resumes between Henry II of France and Philip II of Spain.
November 5 – Second Battle of Panipat: Fifty miles north of Delhi, a Mughal army defeats the forces of Hemu, to ensure Akbar the throne of India.
The kings of Spain take control of the Flanders region, including what is now the French département of Nord.
The Plantations of Ireland are started in King's County (now County Offaly) and Queen's County (now County Laois), the earliest attempt at systematic ethnic cleansing in Ireland, by the Roman Catholic ruler Queen Mary I of England.
Future King John III of Sweden becomes ruler of Finland as Duke John.
Ivan the Terrible conquers Astrakhan, opening the Volga River to Russian traffic and trade.
Welser banking families of Augsburg lose colonial control of Venezuela.
Lorenzo Priuli becomes Doge of Venice.
The false Martin Guerre appears in the French village of Artigat.
The first printing press in India is introduced by Jesuits at Saint Paul's College, Goa.
January 8 – Uesugi Kagekatsu, Japanese samurai and warlord (d. 1623)
January 24 – Christian Barnekow, Danish noble, explorer and diplomat (d. 1612)
February 4 – Dorothea of Hanau-Münzenberg, German noblewoman (d. 1638)
February 7 – Countess Maria of Nassau (d. 1616)
February 16 – Tōdō Takatora, Daimyo (d. 1630)
February 21 – Sethus Calvisius, German calendar reformer (d. 1615)
March 7 – Guillaume du Vair, French statesman and philosopher (d. 1621)
March 13 – Dirck van Os, Dutch merchant (d. 1615)
April 8 – David Hoeschel, Librarian (d. 1617)
April 9 – Andreas von Auersperg, Carniolan noble and military commander in the battle of Sisak (d. 1593)
April 27 – François Béroalde de Verville, French writer (d. 1626)
May 31 – Jerzy Radziwiłł, Catholic cardinal (d. 1600)
June 6 – Edward la Zouche, 11th Baron Zouche, English politician and diplomat (d. 1625)
June 13 – Pomponio Nenna, Italian composer (d. 1608)
Victoria of Valois, French princess (d. 1556)
Joan of Valois, French princess (d. 1556)
July 9 – Elizabeth Finch, 1st Countess of Winchilsea, English Countess (d. 1634)
July 22 – Otto Henry, Count Palatine of Sulzbach (d. 1604)
July 26 – James Melville, Scottish divine and reformer (d. 1614)
August 10 – Philipp Nicolai, German Lutheran pastor (d. 1608)
August 16 – Bartolomeo Cesi, Italian painter (d. 1629)
August 17 – Alexander Briant, Jesuit martyr (d. 1581)
August 24 – Sophia Brahe, Danish astronomer, horticulturalist (d. 1643)
September 21 – William Harris, English knight (d. 1616)
Charles I, Duke of Elbeuf, French duke and nobleman (d. 1605)
John Dormer, Member of Parliament (d. 1626)
October 24 – Giovanni Battista Caccini, Italian artist (d. 1613)
October 26 – Ahmad Baba al Massufi, Malian academic (d. 1627)
November 15 – Jacques Davy Duperron, French cardinal (d. 1618)
November 25 – John Heminges, English actor (d. 1630)
November 28 – Francesco Contarini, Doge of Venice (d. 1624)
December 5 – Anne Cecil, Countess of Oxford, English countess (d. 1588)
December 17 – Abdul Rahim Khan-I-Khana, Composer (d. 1627)
December 27 – Jeanne de Lestonnac, French saint (d. 1640)
Margaret Clitherow, English Catholic martyr (d. 1586)
Shibata Katsutoyo, Japanese military commander (d. 1583)
Ahmad Baba al Massufi, Sudanese writer and political leader (d. 1627)
March 21 – Thomas Cranmer, Archbishop of Canterbury (burned at the stake) (b. 1489)
April 18 – Luigi Alamanni, Italian poet and statesman (b. 1495)
May 28 – Saitō Dōsan, Japanese warlord (b. 1494)
June 10 – Martin Agricola, German composer (b. 1486)
July 31 – Ignatius of Loyola, Spanish founder of the Jesuit order and saint (b. 1491)
August 11 – John Bell, Bishop of Worcester
September – Patrick Hepburn, 3rd Earl of Bothwell, Scottish traitor (b. 1512)
October 21 – Pietro Aretino, Italian author (b. 1492)
November 10 – Richard Chancellor, English Arctic explorer (drowned at sea) (b. c.1521)
November 14 – Giovanni della Casa, Italian poet (b. 1503)
Tullia d'Aragona, Italian poet, author and philosopher (b. 1510)
Girolamo da Carpi, Italian painter (b. 1501)
Fuzûlî, Turkish poet (b. 1494)
Brian mac Cathaoir O Conchobhair Failghe, last of the Kings of Ui Failghe
Jacob Clemens non Papa, Flemish composer (b. 1510)
Year 1556 (MDLVI) was a leap year starting on Wednesday (link will display the full calendar) of the Julian calendar.