The year 1558 in science and technology included a number of events, some of which are listed here.

• November – Thomas Gresham states Gresham's law.^[1][2]

• English explorer Anthony Jenkinson travels from Moscow to Astrakhan and Bokhara.^[1] He is the first Englishman to note that the Amu Darya changed course to start flowing into the Aral Sea.^[3]

• Venetian composer Gioseffo Zarlino accurately describes meantone temperament in Le istitutioni harmoniche.^[1]

• Giambattista della Porta publishes the popular science book Magia Naturalis in Naples.
• First publication of Petrus Peregrinus de Maricourt's 13th century Epistola de magnete, edited by Achilles Gasser and printed in Augsburg.

• September 4 – John Feild receives a confirmation of arms in England and the grant of a crest allusive to his attainments in astronomy.

• Robert Alaine, English astronomer (died 1603)
• André du Laurens, French physician and gerontologist (died 1609)
• Olivier van Noort, Dutch circumnavigator (died 1627)

• March 6 – Luca Gaurico, Italian astrologer (born 1476)
• March 6 – Fray Marcos de Niza, Savoyard Franciscan explorer (born c. 1495)
• October 21 – Julius Caesar Scaliger, Italian-born polymath (born 1484)
• Jean Fernel, French physician (born 1497)
• Robert Recorde, Welsh-born physician and mathematician (born c. 1512)
• approx. date
  • Álvar Núñez Cabeza de Vaca, Spanish anthropologist (born c. 1488/90)