In its major summer exhibition, opening next week, the National Gallery of Australia will be telling the story of the lifelong exchange between these two towering figures of modern art.

Between them, they set the course of western art history in the first half of the 20th century, where Renaissance one-point perspective and Realism were abandoned for radical ideas about depicting the "third dimension".

Both envisaged a new future for art.

The exhibition examines the intersecting paths of the two artists over the years, and the way they each responded to the other's work. No one was more attentive and aware of Matisse's art than Picasso and vice versa. Both explored issues of space, movement, form, colour and figurative and abstract art, and then borrowed from each other to improve their own art.

Their association was one of mutual awareness, recognition and artistic companionship, combined with a sense of competitiveness. This artistic rivalry and collaboration began the new story of modernism.

While both artists shared the determination to pursue new directions in art, they came from very different worlds.

Matisse experienced a conservative upbringing in northern France. After studying law in Paris and working as an articled clerk, his world changed when his mother gave him a paint box at the age of 20. Discovering a passion and a talent for art, he abandoned his law career and embraced a new ambition to study art in Paris.

By 1901 Matisse was the leader of the newest art movement, the Fauves (French for "wild beast"). Influenced by the post-impressionists, Fauvism was dominated by solid forms and vivid colour applied with bold brushwork that evoked emotion and created an abstract sense of space.

Twelve years younger than Matisse, Picasso was a childhood prodigy from southern Spain, nurtured and supported by his artistic family. As a young man, he moved to Paris to establish his name in the capital of the art world.

He initially adopted a modern fin-de-siècle style, inspired by Edgar Degas and Henri de Toulouse-Lautrec's imagery of cabaret culture, brothel scenes and women at a bar or in a laundry. This was followed by his Blue Period; imbued with dark and gloomy blues, his paintings reflect the poverty many people experienced at this time.

Although Matisse and Picasso saw each other regularly after their first meeting, Matisse was threatened by the arrival of the younger artist, and feared that his position as a leading artist was in jeopardy. Despite their differences, both artists were united in their admiration of Paul Cézanne, who challenged the traditional one-point perspective by deconstructing three-dimensional forms on a two-dimensional plane. Their mutual rivalry was exacerbated by their different interpretations of the master.

After Matisse and Picasso's initial battle for supremacy played out early in the century, a period of intense borrowing followed, as the artists began to respond and feed off each other. Perceiving the limitations of Picasso's early Cubism, Matisse responded with greater emphasis on movement and the interaction of figures.

Despite his aversion towards Picasso's radical approach, he began to reconsider his talented rival's achievements and experimented with incorporating the forms and muted palette of Cubism in his work.

From 1912, Picasso became increasingly dissatisfied with the restricted colour and static geometry of Analytic Cubism. His compositions began to change, first using a fractured effect and finally into multifaceted forms.

In the wake of Matisse's large, dynamic and vivid figurative paintings, Picasso recognised his rival's power as a stellar colourist, whose layered forms were rich in textures.

Meanwhile, in another artistic setting, Sergei Diaghilev, impresario of the Ballets Russes, had been shocking audiences for more than 20 years with his ballet company's daring fusion of music, dance and art. He collaborated on the company's set and costume designs with leading modern artists, including Picasso and Matisse.

Picasso was the first to succumb to Diaghilev's powers of persuasion. The two were introduced by French writer Jean Cocteau, with whom they collaborated on the 1917 cubist ballet Parade. After marrying Olga Khokhlova, one of the company's principal dancers, Picasso returned to Spain with Diaghilev and choreographer Leonide Massine. He drew on his Spanish roots for the design of the Ballets Russes production Le Tricorne.

Its premier at the Alhambra Theatre in London in 1919 met with unanimous praise and it became a mainstay of the company's repertoire. Picasso's original designs were revived for performances at the height of the Spanish Civil War in 1934.

But while Picasso threw himself into life working for Diaghilev, Matisse had to be cajoled. The shadow cast by the critical success of Le Tricorne finally persuaded Matisse to work with the Ballets Russes in 1919 on Le Chant du rossignol [The song of the nightingale]. For Matisse, the project was extremely fraught. He felt pressure to create something more wonderful and popular than Picasso, and was constricted by Diaghilev's controlling oversight. Caught between emulating the ornate style typical of early Ballets Russes productions and taking a starker, more modernist approach, he attempted to do both, an approach derided by critics.

After the devastation of the First World War, life changed dramatically for Matisse and Picasso. A middle-aged Matisse abandoned his family, turned his back on the Parisian art scene and he went to live alone in Nice.

Picasso left his bohemian lifestyle for what his friend, writer Max Jacob called his Duchess period (l'époque des duchesses), presided over by his wife, Olga Khokhlova. Both artists returned to a figurative style and a more traditional depiction of space.

Picasso travelled to Italy where he viewed Roman copies of Greek sculpture. In response to both visual and literary sources, he adopted classical forms and gestures to create figures in delicate line drawings and prints. Picasso spent the summer of 1922 in Fontainebleau, where he drew on his imagination to depict monumental classical figures with a strong sculptural quality. He also produced late-cubist compositions with curvilinear forms to evoke movement, adopting Matisse's layering methods and interest in texture and colour.

As a student, Matisse copied paintings at the Louvre, particularly Renaissance artists, as well as sculpture by Michelangelo. In the latter part of the 1920s Matisse, following Picasso's example, renewed his interest in the classical tradition in painting, sculpture and printmaking. He also became fascinated with the warm Mediterranean light, and infused his works with sunlight flooding through the windows of his Nice studio.

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Living in the south of France, Matisse adopted a naturalistic style. As the 1920s advanced, his compositions became bolder with a series of odalisques that illustrated his debt to Jean-Auguste-Dominique Ingres and Eugène Delacroix. Matisse evoked an exotic world. His works were constructions of his imagination-a series of beautiful models dressed in costumes in elaborate stage settings filled with wall hangings, screens, rugs, domestic utensils and furniture, many from his own collection of Islamic decorative arts.

By the mid-1920s Picasso was invading Matisse's territory of the orient, without his reverence to past traditions or Islamic content. After 10 years of marriage, Picasso's feelings for Olga Khokhlova had turned to contempt. In a punishing estimation of their relationship, and a cruel jab at Matisse, Picasso created an image of his wife as a screeching odalisque, naked and reclining on a chair in a sumptuously ornate Matisse-style interior.

Both artists were deeply affected by the tense political situation during the Second World War. Picasso spent most of the war in Paris, living between the homes he shared with Marie-Thérèse Walter and their daughter Maya, and his new lover, photographer Dora Maar. For Matisse, after many years of living apart from his wife, his marriage ended and he returned permanently to Nice with his studio assistant, Lydia Delectorskaya.

Over time, Matisse and Picasso no longer felt the need to compete with each other to be first with the newest and most radical ideas. Each artist now had the freedom to exercise their imagination.

In January 1941, 72 year-old Matisse underwent emergency surgery for colonic cancer. Anticipating that he wouldn't survive, he was more than pleasantly surprised when he did. The experience gave him a sense of rebirth. Unable to concentrate on painting, Matisse set out on a new journey making papercuts, which he composed from his bed or in a wheelchair.

In a process he considered to be an amalgam of painting, sculpture and drawing, he 'carved' his coloured paper into various shapes using textile shears. His new art form was characterised by brilliant colour, distilled forms and often large-scale compositions, and became his major focus in his last years.

After Matisse died in 1954, Picasso displayed an early lack of interest in the death of his rival. Ultimately, however, his response to the loss was an artistic one, painting a series of homages to Matisse's love of the Middle East and North Africa. In these paintings, Picasso adopted many of Matisse's favoured motifs-the odalisque, the open window with a view to the outside world and Islamic decorative arts.