Anton Exner was the most important dealer, collector and assessor of East Asian art in Vienna between the wars. His collection included all branches of Asian – particularly Chinese and Japanese – art from all epochs. He worked his way up from modest circumstances. He had no formal higher education, and his expertise was self-taught. During a long sojourn in Canada and the USA from 1908 to 1910, he made contact for the first time with Chinese dealers. On the return voyage on a cargo ship, he acquired handicrafts and Japanese silk blouses at various Asian ports, which formed the basis for his future business activities in Vienna. From then on he went almost every year on buying trips to the Far East. From around 1912, he worked from his home at Lerchenfelderstraße 66 in Vienna's 8th district and from 1929 in the house he had acquired at Paniglgasse 18–20 in the 4th district. As he was returning from Asia in summer 1914, he was taken by surprise by the start of the First World War. He muddled through in the USA, opening an Asian art business on 56th Street in New York. He was interned for a time as an enemy alien. It was not until the end of 1919 that he was able to return to Vienna. The Dorotheum appointed him as a sworn assessor of Asian art, a position he held for around a quarter of a century. From the early 1920s, he lent objects for all major exhibitions of Asian art in Vienna. Exner's family origins in the Sudetenland influenced his ideological beliefs. He had long been a supporter of pan-German nationalism and joined the NSDAP in 1931 (membership number 782343). He remained a member even when the Party was banned but also joined the Vaterländische Front (Fatherland Front). During the Nazi era, he often evaluated Asian art from collections expropriated from Jews, particularly for auctions in the Dorotheum. In 1938, with the support of the Reichsstatthalterei (especially its state secretary for cultural affairs at the time Kajetan Mühlmann), the idea of an Asian art museum in Vienna was put forward, with Exner's collection providing the basis. Anton Exner and his son Walter Exner were the driving forces behind the museum and were to have leading functions in it. The project was abandoned above all because of the opposition of the Staatliches Kunstgewerbemuseum in Wien (State Arts and Crafts Museum in Vienna), as it would have had to give up its own Asian art holdings. At the beginning of 1939, Anton Exner offered to lend some of his Asian art collection to the museum. The museum chose the objects it wanted and an agreement was concluded. In 1943 a major exchange took place between Exner and the Kunstgewerbemuseum, with the museum swapping above all Asian export and commercial items from the former Handelsmuseum (trade museum) for valuable applied art items. In 1944 Exner signed a notarized document transforming the temporary loan into a lifetime loan and donation in the event of his death. This "first donation" consisting of 2,195 objects was not agreed with Anton's son Walter Exner, who had been conscripted into the Wehrmacht. A letter of protest by Walter Exner to the museum in 1944 was not followed up.

In June 1945 Anton Exner was arrested as a former Nazi and brought to trial before a Volksgericht for membership of the NSDAP during the period of illegality (§ 10 of the Prohibition Act) and suspicion of illegal enrichment (§ 6 of the War Criminals Act). The case also dealt with the Aryanization of Wilma Werner's art dealership in Vienna city centre by Anton Exner's daughter, Edith Schmaelz, thought to have been at Exner's instigation. On application of the Kunstgewerbemuseum the remainder of Exner's private collection was secured by the state and transferred to Dorotheum depots. In a police report, Anton Exner offered on 28 June 1945 to give the objects to the Republic. In 1946 he confirmed this "second donation" with legally binding force, again without the agreement of his son, who had helped compile the collection. Year-long efforts by Walter Exner to obtain his share of the donation from the MAK came to nothing. The Volksgericht case against Anton Exner and several close relatives was dropped. The MAK currently owns around 3,700 mostly very valuable objects from the Exner collection, and the Weltmuseum Wien 177 inventory numbers with the same provenance. Provenance research is complicated in particular by the fact that there are no reliable details of previous owners and dealers, and it remains unclear which objects were acquired during the numerous buying trips by Anton (and Walter) Exner and which were acquired in Austria and other European countries, particularly during the Nazi era. Although Anton Exner wrote to the Österreichisches Museum für angewandte Kunst (Austrian Museum of Applied Arts) in 1948 that as far as he knew there were no expropriated items in his collection, the museum restituted a number of objects from the Exner collection in the second half of the 1940s and the 1950s that had been part of the collections of Klara Mertens-Steiner, Ernst Dub, Richard E. Weiss and Caroline (Karoline) Czeczowiczka.