Copenhagen is the capital and most populous city of Denmark. The city is the cultural, economic and governmental centre of Denmark. With a number of bridges connecting the various districts, the cityscape is characterised by parks, promenades, and waterfronts. Copenhagen's landmarks such as Tivoli Gardens, The Little Mermaid statue, the Amalienborg and Christiansborg palaces, Rosenborg Castle, Frederik's Church, Børsen and many museums, restaurants and nightclubs are significant tourist attractions.

Apart from being the national capital, Copenhagen also serves as the cultural hub of Denmark and wider Scandinavia. Since the late 1990s, it has undergone a transformation from a modest Scandinavian capital into a metropolitan city of international appeal in the same league as Barcelona and Amsterdam. This is a result of huge investments in infrastructure and culture as well as the work of successful new Danish architects, designers and chefs. Copenhagen Fashion Week, the largest fashion event in Northern Europe, takes place every year in February and August.

Copenhagen has a wide array of museums of international standing. The National Museum, Nationalmuseet, is Denmark's largest museum of archaeology and cultural history, comprising the histories of Danish and foreign cultures alike. Denmark's National Gallery (Statens Museum for Kunst) is the national art museum with collections dating from the 12th century to the present. In addition to Danish painters, artists represented in the collections include Rubens, Rembrandt, Picasso, Braque, Léger, Matisse, Emil Nolde, Olafur Eliasson, Elmgreen and Dragset, Superflex and Jens Haaning.

Another important Copenhagen art museum is the Ny Carlsberg Glyptotek founded by second generation Carlsberg philanthropist Carl Jacobsen and built around his personal collections. Its main focus is classical Egyptian, Roman and Greek sculptures and antiquities and a collection of Rodin sculptures, the largest outside France. Besides its sculpture collections, the museum also holds a comprehensive collection of paintings of Impressionist and Post-Impressionist painters such as Monet, Renoir, Cézanne, van Gogh and Toulouse-Lautrec as well as works by the Danish Golden Age painters.

Louisiana is a Museum of Modern Art situated on the coast just north of Copenhagen. It is located in the middle of a sculpture garden on a cliff overlooking Øresund. Its collection of over 3,000 items includes works by Picasso, Giacometti and Dubuffet. The Danish Design Museum is housed in the 18th-century former Frederiks Hospital and displays Danish design as well as international design and crafts.

Other museums include: the Thorvaldsens Museum, dedicated to the oeuvre of romantic Danish sculptor Bertel Thorvaldsen who lived and worked in Rome; the Cisternerne museum, an exhibition space for contemporary art, located in former cisterns that come complete with stalactites formed by the changing water levels; and the Ordrupgaard Museum, located just north of Copenhagen, which features 19th-century French and Danish art and is noted for its works by Paul Gauguin.

The new Copenhagen Concert Hall opened in January 2009. Designed by Jean Nouvel, it has four halls with the main auditorium seating 1,800 people. It serves as the home of the Danish National Symphony Orchestra and along with the Walt Disney Concert Hall in Los Angeles is the most expensive concert hall ever built. Another important venue for classical music is the Tivoli Concert Hall located in the Tivoli Gardens. Designed by Henning Larsen, the Copenhagen Opera House (Operaen) opened in 2005. It is among the most modern opera houses in the world. The Royal Danish Theatre also stages opera in addition to its drama productions. It is also home to the Royal Danish Ballet. Founded in 1748 along with the theatre, it is one of the oldest ballet troupes in Europe, and is noted for its Bournonville style of ballet.

Copenhagen has a significant jazz scene that has existed for many years. It developed when a number of American jazz musicians such as Ben Webster, Thad Jones, Richard Boone, Ernie Wilkins, Kenny Drew, Ed Thigpen, Bob Rockwell, Dexter Gordon, and others such as rock guitarist Link Wray came to live in Copenhagen during the 1960s. Every year in early July, Copenhagen's streets, squares, parks as well as cafés and concert halls fill up with big and small jazz concerts during the Copenhagen Jazz Festival. One of Europe's top jazz festivals, the annual event features around 900 concerts at 100 venues with over 200,000 guests from Denmark and around the world.

The largest venue for popular music in Copenhagen is Vega in the Vesterbro district. It was chosen as "best concert venue in Europe" by international music magazine Live. The venue has three concert halls: the great hall, Store Vega, accommodates audiences of 1,550, the middle hall, Lille Vega, has space for 500 and Ideal Bar Live has a capacity of 250. Every September since 2006, the Festival of Endless Gratitude (FOEG) has taken place in Copenhagen. This festival focuses on indie counterculture, experimental pop music and left field music combined with visual arts exhibitions.

Copenhagen has a wide selection of art museums and galleries displaying both historic works and more modern contributions. They include Statens Museum for Kunst, i.e. the Danish national art gallery, in the Østre Anlæg park, and the adjacent Hirschsprung Collection specialising in the 19th and early 20th century. Kunsthal Charlottenborg in the city centre exhibits national and international contemporary art. Den Frie Udstilling near the Østerport Station exhibits paintings created and selected by contemporary artists themselves rather than by the official authorities. The Arken Museum of Modern Art is located in southwestern Ishøj. Among artists who have painted scenes of Copenhagen are Martinus Rørbye (1803–1848), Christen Købke (1810–1848) and the prolific Paul Gustav Fischer (1860–1934).

A number of notable sculptures can be seen in the city. In addition to The Little Mermaid on the waterfront, there are two historic equestrian statues in the city centre: Jacques Saly's Frederik V on Horseback (1771) in Amalienborg Square and the statue of Christian V on Kongens Nytorv created by Abraham-César Lamoureux in 1688 who was inspired by the statue of Louis XIII in Paris. Rosenborg Castle Gardens contains several sculptures and monuments including August Saabye's Hans Christian Andersen, Aksel Hansen's Echo, and Vilhelm Bissen's Dowager Queen Caroline Amalie.

Copenhagen is believed to have invented the photomarathon photography competition, which has been held in the City each year since 1989.