The idea of influence is so broad, so ubiquitous and so often misused that it may be the most misleading concept with which we try to make sense of art and art history. Artists may be influenced by things they love, and by things they hate; they may be deeply influenced by precursors with whom they share no identifiable affinities of content or style; and they may produce work that seems superficially identical to that of another artist even when there was no contact, no intent to imitate, and no similarity of purpose or message.

The Phillips Collection has chosen two different words — riffs and relations — for the title of a new exhibition that traces the influence of modernism on African American artists in the 20th and 21st centuries. “Riffs” suggests something that is spontaneously inspirational, a jumping-off point for elaboration or development of a modernist idea or image; “relations,” a wide-open term full of ambiguity, gets at the deeper problem of tracing influence, both negative and positive.

The emotions inspired by the absorbing exhibition, “Riffs and Relations: African American Artists and the European Modernist Tradition,” are both deeply negative and positive. Curator Adrienne L. Childs tells a story dating back to the beginning of the 20th century, when such artists as Picasso, Braque and Matisse turned to African art for new ideas about how to represent the world, creating figures with masklike faces, flattened forms and backgrounds of vibrant patterning. They weren’t just borrowing visual ideas, however. Many of them believed in a connection between what they saw as primitive culture and the deeper wellsprings of psychological life, a way to reference and represent urges and emotional drives that had been suppressed by “civilization.”

But they also were appropriating wholesale the visual material of people who were suffering colonial oppression, taking sacred objects out of context and imputing to them European-derived ideas about their purpose and meaning. It was theft and homage, with all the damage of the theft incurring to those who were often powerless, and the homage paid not to any artist or culture in particular, but generally to an idea of Africa that was invented to serve European needs.

The story becomes complicated right from the start, in part because the initial appropriation of African ideas was so successful, visually, within the context of European art. It led to an explosion of ideas and forms, influential across almost the whole spectrum of Western creativity. And it happened at a moment when African American artists were beginning to assert their presence within that milieu, and looking for ways to consolidate a sense of identity in an art world that largely rejected them. So the initial appropriation led to re-appropriation, as African American artists repurposed what the European artists had initially borrowed.

In 1925, Alain Locke, the “dean” of the Harlem Renaissance, published a volume of essays called “The New Negro,” which encouraged African American artists to look to newly invigorated European modernist artists, the same ones who were making hay with “primitivism,” for inspiration. Herein were possible sources for a new African American idiom, connected both to contemporary art currents and authentic African culture. It was an exhortation that paralleled what European countries had done over the past century — raiding their own folk culture to invent new national identities — but the idea that African visual ideas processed by European artists was a route to authentic African culture was questionable.

Still, it was a way forward, and artists, especially those struggling against larger cultural forces, are mainly looking for just that, a way forward. One sees that frequently throughout this exhibition. Artists find what they need, and what they need can come from unlikely places. In 1921, several years before Locke’s influential treatise, Hale Woodruff, one of the greatest 20th-century African American artists, laid his hands on a book about African sculpture published in Germany. That book, “Afrikanische Plastik,” included black and white plates of African ceremonial figures, sculpted heads and stools, and a long essay in German that Woodruff couldn’t read.

But it was the visual stimulus he needed, and it helped him move forward on a brilliant path. Among the most exciting works on view in the Phillips exhibition is Woodruff’s circa 1958 “Africa and the Bull,” which reimagines a well-used European trope — the Rape of Europa — in African terms, with a black figure riding a white bull. The complexity of Woodruff’s representation of the bull, in a de Kooning palette of grays, is a magnificent foil to the black and white floral figures that envelope the image of Africa.

The exhibition traces the complex back-and-forth between artists up to the current moment, in which artists are engaged in much more direct critique of the modernist inheritance. Titus Kaphar uses thick fields of black tar to encroach on the morally obtuse prettiness of Impressionism, forcing viewers to confront the cost of European wealth and luxury — in large measure derived from global exploitation. What is missing from these colorful Impressionist paintings that are so beloved by museum audiences? Not just African figures, but also the history of Africa, transpiring with substantial misery so far away at the same time that Monet was painting women with parasols in green fields speckled with flowers.

The history of African American engagement with modernism also includes internal arguments and complications. By the 1960s and ’70s, an older generation of artists who found much to admire in abstraction — including the freedom to say just as much or as little as they wanted about the so-called real world — were being confronted by more politically active younger artists. Artists who favored muted colors, or grid-like forms, or allover fields of pattern and color, didn’t seem sufficiently engaged with what was happening on the streets. Groups like the Black Arts Movement were looking for new forms and new ideas that weren’t constrained by the aesthetic dictates of the still white-dominated fine arts world.

The argument wasn’t new, and it continues today in different forms, across all kinds of creative media. One of the most arresting images in the exhibition, an untitled circa 1958 abstraction by Beauford Delaney, is a burst of yellow, orange and red, with subtle blue tones in the interstices of a vibrant field of brush work. It was made after Delaney, a gay black man, moved to Paris, where he changed from making figurative work to mostly abstract compositions. It is placed close to one of the Phillips’s prized van Goghs, the 1889 “The Road Menders,” with which it shares a similar color scheme.

In 1945, before Delaney went to France, while he was still living a dual life as a gay artist in Greenwich Village and a black artist in Harlem, he was the subject of a rapturous profile by Henry Miller, in Miller’s trademark freely associative, subjective and sometimes self-indulgent style. Miller admired Delaney, and to express that admiration he noted how much more difficult it was for a black artist, a product of the Jim Crow South, to take the chances, with color and form, that Delaney was taking. By avoiding cliches, by aspiring to greatness, by challenging white audiences, he would inevitably be neglected, ostracized or forgotten: “That makes him just another ‘crazy n-----,’ ” Miller wrote, using the racial slur as if it were spoken by a generic white racist and philistine.

Delaney was mostly forgotten for a long time. He died an alcoholic, poor and confined to a mental hospital in Paris in 1979. Fifteen years later, an article in “Art in America” was titled “Whatever Happened to Beauford Delaney?”

Miller’s article is full of admiration, both for Delaney, and self-admiration, for his own ability to appreciate Delaney’s genius. Delaney, he argued, transcended the world in which he struggled: “There was no black and white, no master or slave; there was just the endless stretch of vision in which the imagination of all men dwells.”

Miller got that wrong in so many ways. Standing in the Phillips Collection, looking at Delaney’s painting, I wonder not just how one makes amends for the world Delaney lived in, but also for the myriad ways in which even seemingly innocent forms of admiration are channeled through social structures that warp and corrupt it into yet more forms of oppression.

Riffs and Relations: African American Artists and the European Modernist Tradition Through May 24 at the Phillips Collection.