1. Marcel Duchamp, Fountain, 1917, Tate Modern, London

Duchamp’s Fountain is a urinal the artist found and inscribed with the signature R. Mutt. It is considered to be a major landmark in 20th century art in that it probes viewers to reconsider what exactly it is that makes an object a work of art. The piece is referred to as a readymade or found art object.

Duchamp’s Fountain in its seminal turning upside down of assumptions with regards to authorship and creation remains important and puzzling today. Art history is a discipline that constantly questions its subject matter. What constitutes a work of art and, more pertinently, what makes a work of art good, bad, or important are questions that never seem to be put to rest and the consideration contemporary historians give to Duchamp’s oeuvre is testament to this fact.

2. Damien Hirst, The Physical Impossibility of Death in the Mind of Someone Living, 1991, Private Collection

Hirst’s conceptual piece, The Physical Impossibility of Death in the Mind of Someone Living features a 13-foot tiger shark in a glass tank of formaldehyde. Like Duchamp’s urinal it is a readymade in that it is comprised of objects already existing in the world. It is controversial for a variety of reasons.

First, it captured a record-breaking price at auction despite its taking conceptualism to a limit many people considered absurd. Second, the fact that Hirst took his work directly to auction rather than selling it through a gallery. Furthermore, after its purchase and installation in a private home the piece began to leak formaldehyde thereby requiring repairs.

Debate ensued over whether or not repairing the piece would mar the artistic integrity of the work. Ultimately repair was not seen as endangering the work’s originality in that the essence of the work was said to be the theories upon which it was built rather than its physical substance.

3. Pablo Picasso, Les Demoiselles d’Avignon, 1907, Museum of Modern Art, New York

Today Pablo Picasso’s cubist pictures and allusions to African art no longer appear surprising or shocking. The way in which he distorted forms and the human figure as well as his unrealistic use of color no longer affronts our general conceptions regarding “good” art. In 1907, however, the Les Demoiselles d’Avignon outraged the public and art-world officials alike. The work appeared crude, unfinished, and hugely unsettling.

Today the work can still be seen as controversial in that experts remain at odds with respect to its influences and Picasso’s intention in painting it. Some historians interpret the work as exhibiting Picasso’s crippling fear of contracting a venereal disease, a fear that becomes manifest with his “cruel” depiction of the violent-looking female brothel workers. Other historians view the work as a formal working through of certain motifs Picasso borrowed from Cezanne and African art.

4. Gustav Klimt, Portrait of Adele Bloch-Bauer, 1907, Neue Galerie, New York

This work is controversial not because of its content or the manner in which it was painted, but because of its art-market history. The portrait, of Adele Bloch-Bauer, the wife of a wealthy Jewish leader of industry, is considered one of the Gustav Klimt’s masterpieces. When Germany annexed Austria in March 1938, Mr. Bloch-Bauer fled, leaving all of his possessions including this painting behind. The Nazi government confiscated his property and placed three of the paintings in an Austrian Gallery and sold the rest.

For many years this work was the focus of a restitution battle between the Austrian government and a nice of Mrs. Bloch Bauer. In 2000 Mrs. Altmann, Bloch-Bauer’s niece, sued the Austrian government. After much back and forth, the suit ended up in the United States Supreme Court, which ultimately decided in favor of Mrs. Altmann and her fellow heirs. Many museums approached the heirs to purchase the work.

Ultimately the heirs put the work up at auction and to their great happiness cosmetics magnate Ronald S. Lauder bought the painting and installed it in his 5th Avenue museum, the Neue Gallerie, a museum dedicated to German and Austrian art and culture. The painting was bought for $135 million, the highest sum ever paid for a painting.

5. Takashi Murakami, works from the “Hiropon Factory,” since 2001

Takashi Murakami is often compared to Andy Warhol. Both Warhol and Murakami play with elements of high and low culture. Like Warhol, Murakami takes motifs and characters from low culture, reconfigures it, and sells it as “high-art” at market.

Murakami does not stop at the art market, however. He has pushed the union between consumerism and art to its limit by selling his work or, rather, works from his “factory” in the form of videos, T-shirts, phone caddies and, most recently, $5,000 Louis Vuitton handbags.

The mass production of Murakami’s art in addition to the way in which he simultaneously sells his work as luxury goods, low-market knick-knacks, and as fine art at auction makes his oeuvre very controversial.