Mozart's musical ability started to become apparent when he was a toddler. He was the son of Leopold Mozart, one of Europe's leading musical pedagogues, whose influential textbook Versuch einer gründlichen Violinschule ("Essay on the fundamentals of violin playing") was published in 1756, the same year as Mozart's birth. Mozart received intensive musical training from his father, including instruction in both the piano and violin. Musically, he developed very rapidly and began to compose his own works at the age of five.

Leopold soon realized that he could earn a substantial income by showcasing his son as a Wunderkind in the courts of Europe. Mozart gained fame as a prodigy capable of playing blindfolded or with his hands behind his back, and for his ability to improvise wonderfully and at length on difficult passages he had never seen before. His older sister, Maria Anna, nicknamed "Nannerl", was a talented pianist and often accompanied her brother on Leopold's tours. Mozart wrote a number of piano pieces, in particular duets and duos, to play with her. On one occasion when Mozart became ill, Leopold expressed more concern over the loss of income than over his son's well-being. Constant travel and cold weather may have contributed to his subsequent illness later in life.

During his formative years, Mozart completed several journeys throughout Europe, beginning with an exhibition in 1762 at the Court of the Elector of Bavaria in Munich, then in the same year at the Imperial Court in Vienna. A long concert tour soon followed (three and a half years), which took him with his father to the courts of Munich, Mannheim, Paris, London, The Hague, again to Paris, and back home via Zürich, Donaueschingen, and Munich. They went to Vienna again in late 1767 and remained there until December 1768.

After one year spent in Salzburg, three trips to Italy followed: from December 1769 to March 1771, from August to December 1771, and from October 1772 to March 1773. During the first of these trips, Mozart met G.B. Martini in Bologna, and was accepted as a member of the famous Accademia Filarmonica. A highlight of the Italian journey, which is now an almost legendary tale, occurred when he heard Gregorio Allegri's Miserere once in performance, then wrote it out in its entirety from memory, only returning a second time to correct minor errors.

In September of 1777, accompanied only by his mother, Mozart began a tour of Europe that included Munich, Mannheim, and Paris, where his mother died.

During his trips, Mozart met a great number of musicians and acquainted himself with the works of other great composers. He came to know the work of J.S. Bach and G.F. Handel; and he met Joseph Haydn, who declared to Leopold, "Before God and as an honest man I tell you that your son is the greatest composer known to me either in person or by name. He has taste and, what is more, the most profound knowledge of composition.". Even non-musicians caught Mozart's attention: he was so taken by the sound created by Benjamin Franklin's glass harmonica that he composed several pieces of music for it.