Giuseppe Crespi was born in Bologna to Girolamo Crespi and Isabella Cospi.

His mother was a distant relation of the noble Cospi family, which has ties to the Florentine House of Medici.

He is nicknamed "the Spanish One" (Lo Spagnuolo) because of his habit of wearing tight clothes characteristic of Spanish fashion of the time.

He was apprenticed by age twelve with Angelo Michele Toni (1640–1708).

He had worked from the ages of fifteen to eighteen under the Bolognese Domenico Maria Canuti.

The Roman painter Carlo Maratti, on a visit to Bologna, is said to have invited Crespi to work in Rome, but Crespi declined.

Maratti's friend, the Bolognese Carlo Cignani, had invited Crespi in 1681–82 to join an Accademia del Nudo for the purpose of studying drawing, and he had remained in that studio until 1686, when Cignani relocated to Forlì and his studio was taken over by Canuti's most prominent pupil, Giovanni Antonio Burrini.

Crespi from this time hence has worked independently of other artists.

He is said to have had a camera optica in his house for painting.

He had by the 1690s completed various altarpieces, including a Temptation of Saint Anthony commissioned by Count Carlo Cesare Malvasia, now in San Niccolò degli Albari.

He has journeyed to Venice, but surprisingly, never to Rome.

Bearing his large religious canvas of Massacre of the Innocents and a note from Count Vincenzo Rannuzi Cospi as an introduction, Crespi had fled in the middle of the night to Florence in 1708, and gained the patronage of the Grand Duke Ferdinand I de' Medici.

He had been forced to flee Bologna with the canvas, which while intended for the Duke, had been fancied by a local priest, Don Carlo Silva, for himself.

The events surrounding this episode have become the source of much litigation, in which Crespi, at least for the next five years, finds the Duke a firm protector.