Events of 1378 
 March – In England, John Wycliffe tries to promote his ideas for Catholic reform by laying his theses before parliament and making them public in a tract. He is subsequently summoned before Archbishop of Canterbury, Simon of Sudbury, at the episcopal palace at Lambeth to defend his actions.
 September 20 – Unhappy with Pope Urban's critical attitude towards them, the majority of the cardinals meet at Fondi and elect Clement VII as antipope and establish a rival papal court at Avignon. This split within the Catholic Church becomes known as the Western Schism.

Undated 
 Holy Roman Emperor Charles IV meets with his nephew Charles V of France to publicly celebrate the friendship between their two nations.
 Holy Roman Emperor Charles IV dies and is succeeded by his son, Wenceslaus.
 The Papacy makes a permanent move back from Avignon to Rome, ending the Avignon Papacy.
 Pope Gregory XI dies. Due to riots in Rome calling for a Roman pope, the cardinals, who were mostly French, elect Pope Urban VI (Bartolomeo Prignano, Archbishop of Bari) as the 202nd Pope.
 France, Aragon, Castile and León, Cyprus, Burgundy, Savoy, Naples and Scotland choose to recognise Antipope Clement VII. Denmark, England, Flanders, the Holy Roman Empire, Hungary, northern Italy, Ireland, Norway, Poland and Sweden continue to recognise Pope Urban VI.
 Dmitri Donskoi of Moscow & Vladimir resists a small invasion by the Mongol Blue Horde.
 Revolt of the Ciompi – discontent wool carders briefly take over the government of Florence. For the first time, a European government represents all social classes.
 Tokhtamysh dethrones Timur Malik as Khan of the White Horde.
 Kara Osman establishes the Turkomans of the White Sheep dynasty at Diyarbakır in present-day southeast Turkey.
 The Turks capture the town of Ihtiman in west Bulgaria.
 An English spy assassinates Owain Lawgoch, claimant to the throne of Wales and ally of France.
 Gian Galeazzo Visconti succeeds his father, Galeazzo II Visconti, as ruler of Milan.
 Uskhal Khan succeeds his father, Biligtü Khan, as ruler of the Yuan Dynasty in Mongolia.
 Balša II succeeds his father, Durađ I, as ruler of Zeta (now Montenegro).
 Tai Bian succeeds Zhao Bing Fa as King of Mong Mao (now northern Myanmar).
 Appearance of Halley's Comet.
 Da'ud Shah succeeds his assassinated nephew, Aladdin Mujahid Shah, as Bahmani Sultan in present-day southern India. Da'ud Shah is assassinated in the same year and is succeeded by Mohammed Shah II.

Births 
 August 16 – Hongxi Emperor of China (died 1425)
 October 24 – David Stewart, Duke of Rothesay (died 1402)
 December 31 – Pope Callixtus III (died 1458)
 Robert Campin, Flemish painter (died 1444)
 Vittorino da Feltre, Italian humanist (died 1446)
 Lorenzo Ghiberti, Italian sculptor and metal smith (died 1455)
 John Hardyng, English chronicler (died 1465)

Deaths 
 February 6 – Jeanne de Bourbon, queen of Charles V of France (born 1338)
 March 27 – Pope Gregory XI
 May 29 – King Henry II of Castile (born 1334)
 July – Owain Lawgoch, titular Prince of Wales – assassinated (born circa 1330)
 August 16 – San Rocco di Venezia, patron saint of pestilence (born 1340)
 November 29 – Charles IV, Holy Roman Emperor (born 1316)
 Galeazzo II Visconti, Lord of Milan