While he was attending the school of the Caracci his preference for the plastic art became evident, and he placed himself under the instruction of the sculptor Conventi.
He studied at Bologna under Lodovico Caracci and Giulio Conventi.
At the age of twenty he was brought under the notice of Duke Ferdinand of Mantua, who gave him several commissions.
He was also much employed about the same period by jewellers and others in modelling in gold, silver and ivory.
In 1622 he worked at the court of Mantua.
After a short residence in Venice he went to Rome in 1625 with an introduction from the duke of Mantua to the pope's nephew, Cardinal Ludovisi, who employed him for a time in the restoration of, ancient statues.
In 1640 he executed for Pietro Buoncompagni his first work in marble, a colossal statue of San Filippo Neri, with kneeling angels.
The turning point in Algardi's fortune was the accession of Innocent X, of, the Bolognese house of Panfili, to the papal throne in 1644.
In 1650 Algardi met Velasquez, who obtained some interesting orders for his Italian companion in Spain.
In 1650 he finished the tomb of Pope Leo XI and the great marble relief, The Expulsion of Attila, behind the altar of St. Leo, both in St. Peter's, Rome.
A bronze statue of Pope Innocent X in Palazzo dei Conservatorei, Rome, was completed in 1650.
Algardi's Portrait (bust) of Donna Olimpia Pamphili is in the Doria Gallery, Rome.
During the pontificate of Pope Innocent X from 1644 to 1655, Algardi's activity was much intensified.
Thus there are four chimneys by Algardi in the palace of Aranjuez, where also the figures on the fountain of Neptune were executed by him.
In his later years he became very avaricious and amassed a great fortune.
Algardi was also known for his portraiture which shows an obsessive attention to details of psychologically revealing physiognomy in a sober but immediate naturalism, and minute attention to costume and draperies, such as in the busts of Laudivio Zacchia, Camillo Pamphilj, and of Muzio Frangipane and his two sons Lello and Roberto.
In temperament, his style was more akin to the classicized and restrained baroque of Duquesnoy than to the emotive works of other baroque artists. From an artistic point of view, he was most successful in portrait-statues and groups of children, where he was obliged to follow nature most closely. His terracotta models, some of them finished works of art, were prized by collectors. An outstanding series of terracotta models is at the Hermitage Museum, Saint Petersburg.