- The Inquisition's ban on reprinting Galileo's works was lifted in 1718 when permission was granted to publish an edition of his works (excluding the condemned Dialogue) in Florence. In 1741, Pope Benedict XIV authorised the publication of an edition of Galileo's complete scientific works which included a mildly censored version of the Dialogue. In 1758, the general prohibition against works advocating heliocentrism was removed from the Index of prohibited books, although the specific ban on uncensored versions of the Dialogue and Copernicus's De Revolutionibus remained. All traces of official opposition to heliocentrism by the church disappeared in 1835 when these works were finally dropped from the Index. Interest in the Galileo affair was revived in the early 19th century when Protestant polemicists used it (and other events such as the Spanish Inquisition and the myth of the flat Earth) to attack Roman Catholicism. Interest in it has waxed and waned ever since. In 1939, Pope Pius XII, in his first speech to the Pontifical Academy of Sciences, within a few months of his election to the papacy, described Galileo as being among the "most audacious heroes of research... not afraid of the stumbling blocks and the risks on the way, nor fearful of the funereal monuments". His close advisor of 40 years, Professor Robert Leiber, wrote: "Pius XII was very careful not to close any doors (to science) prematurely. He was energetic on this point and regretted that in the case of Galileo.” On 15 February 1990, in a speech delivered at the Sapienza University of Rome, Cardinal Ratzinger (later Pope Benedict XVI) cited some current views on the Galileo affair as forming what he called "a symptomatic case that permits us to see how deep the self-doubt of the modern age, of science and technology, goes today". Some of the views he cited were those of the philosopher Paul Feyerabend, whom he quoted as saying: "The Church at the time of Galileo kept much more closely to reason than did Galileo himself, and she took into consideration the ethical and social consequences of Galileo's teaching too. Her verdict against Galileo was rational and just and the revision of this verdict can be justified only on the grounds of what is politically opportune.” The Cardinal did not clearly indicate whether he agreed or disagreed with Feyerabend's assertions. He did, however, say: "It would be foolish to construct an impulsive apologetic on the basis of such views.” On 31 October 1992, Pope John Paul II acknowledged that the Church had erred in condemning Galileo for asserting that the Earth revolves around the Sun. "John Paul said the theologians who condemned Galileo did not recognize the formal distinction between the Bible and its interpretation.” In March 2008, the head of the Pontifical Academy of Sciences, Nicola Cabibbo, announced a plan to honour Galileo by erecting a statue of him inside the Vatican walls. In December of the same year, during events to mark the 400th anniversary of Galileo's earliest telescopic observations, Pope Benedict XVI praised his contributions to astronomy. A month later, however, the head of the Pontifical Council for Culture, Gianfranco Ravasi, revealed that the plan to erect a statue of Galileo on the grounds of the Vatican had been suspended.  
- According to Stephen Hawking, Galileo probably bears more of the responsibility for the birth of modern science than anybody else, and Albert Einstein called him the father of modern science. Galileo's astronomical discoveries and investigations into the Copernican theory have led to a lasting legacy which includes the categorisation of the four large moons of Jupiter discovered by Galileo (Io, Europa, Ganymede and Callisto) as the Galilean moons. Other scientific endeavours and principles are named after Galileo including the Galileo spacecraft, the first spacecraft to enter orbit around Jupiter, the proposed Galileo global satellite navigation system, the transformation between inertial systems in classical mechanics denoted Galilean transformation and the Gal (unit), sometimes known as the Galileo, which is a non-SI unit of acceleration. Partly because the year 2009 was the fourth centenary of Galileo's first recorded astronomical observations with the telescope, the United Nations scheduled it to be the International Year of Astronomy. A global scheme was laid out by the International Astronomical Union (IAU), also endorsed by UNESCO—the UN body responsible for educational, scientific and cultural matters. The International Year of Astronomy 2009 was intended to be a global celebration of astronomy and its contributions to society and culture, stimulating worldwide interest not only in astronomy but science in general, with a particular slant towards young people. Planet Galileo and asteroid 697 Galilea are named in his honour.