OK, so I think I can answer your question, but I need to correct a few misconceptions and define a few key terms, first. I would hardly characterize Dada (~100 years old), Abstract Expressionism (~70 years old) or even Pop (50+ years old) as "recent." All of these movements are definitely historical, rather than contemporary, in nature. From that start, it becomes somewhat easier to answer the second part of your question, because there is no need to speculate. We know quite well what came after Pop, and that includes Minimalism, post-Minimalism, performance, feminist art, video art, queer art, photo-realism and other returns of the figurative, and, yes, street and graffiti art. There's more, but we're getting close to the twenty-year rule, so that will have to do.

Now, what forces contributed to these three art forms? The question is complicated, in part because Pop could not have happened without Abstract Expressionism, which could not have happened without Dada. This points to the first half of my answer, which is that modern art movements are understood as building upon one another. Modern art since around 1850, beginning with Edouard Manet and the Impressionists, has been animated primarily by a concept known as avant-gardism. Avant garde literally translates from French to mean "advance guard;" you may be familiar with it from military contexts. Avant garde artists saw (see) their purpose as advancing either art or society (or both) through the use of radical experimentation with the forms and meanings of art itself. From that perspective, Dada is an outgrowth of several European art movements of the earlier twentieth century, including most notably Cubism, Futurism, and Expressionism. All three of these movements were at the forefront of an artistic challenging of the truth value of art. What I mean by that is that these artists all began to work with abstraction, the idea that art must not necessarily seek to accurately represent what we might call "objective reality" (eventually many artists and philosophers would conclude that there is no such thing, but that's getting ahead of ourselves). So, Dada, which is characterized by playful (or sometimes deadly serious) absurdity, the use of ready-mades, and other experimentation with the meaning of art, directly descends from, on the one hand, the fractured and distorted view of reality of the cubists and futurists, and, on the other, the expressionists' pioneering use of so-called "primitive" artistic forms in their works, where an African mask or South American religious object could be inserted into a painting of a European subject in order to give it a more "natural" or "authentic" form of humanity.

But, as you are aware, the development of art historical styles does not happen merely in response to other art historical styles. It's also important to remember that these styles do not proceed in so neat and orderly a line as we might usually expect from narratives like the one I'm providing. Even after Marcel Duchamp started making readymades, painters like Fernand Leger kept painting in a Cubist style. Anyway, with those caveats out of the way, one of the primary drivers of the development of Dada was World War I and the ensuing culture of Weimar Germany. For many artists, especially the large numbers of Germans who had fought in the war and returned to a much-changed country, WWI was incredibly disruptive. It ended the long-reigning Hohenzollern monarchy and installed in Germany a fragile constitutional republic, albeit one that faced crippling economic problems due to the Versailles Treaty, and which would soon fall prey to Nazism. This time was a mixture of the hope for democracy embodied by the government in Weimar along with intense cynicism about the war, as well as the bourgeois nature of German (and Western) society. So, the dislocation, the literal mangling of bodies that came about during the war, is usually seen as a strong driver of avant garde aesthetics at this time. Another was leftism (communism, socialism, anarchism, etc.). Artists joined other intellectuals in seeking to find a way out of what they viewed as the destructive, cyclical nature of capitalism. Many artistic experiments were also aimed at reorienting habits of thought, of pointing to a new, more just future.

So, that's Dada. The next on your list is Abstract Expressionism. The art historical explanation is pretty straightforward. Dada's experiments with readymades and automatic art combined with the burgeoning field of psychoanalysis, with its focus on the analysis of dreams, to bring about Surrealism. These artists sought to harness the unconscious mind for making art, and strange, dreamlike imagery dominated their works (Salvador Dali is undoubtedly the most famous, but think also of Giorgio di Chirico and Joan Miro, among others). Surrealism combined with the native American style of modernism, known as Regionalism, to give birth to Abstract Expressionism. This is where the art historical explanation needs support from the historical one. The reason AbEx came to be in the United States is basically Adolf Hitler. Somewhat famously, Hitler was a failed painter, but more to the point he distrusted and feared modern artists, who he viewed as a bunch of Communists and Jews that would undermine the power of his regime. So, he started rounding up modern art and destroying it (or secretly selling it on the international market). Artists, many of whom were Jews and Communists and nearly all of whom could sense the danger they were in, did their best to flee Germany, along with the rest of the intellectuals. They first went to France, Scandinavia, and the Netherlands, then to London. Many ended up in the United States, where they started working at art schools, training the next generation of American artists. So Jackson Pollock is a combination of Dada and Surrealist experiment with form and automatic production of art, along with the swaggering machismo he learned from an early teacher, the American painter Frederick Thomas Hart Benton. In essence, the reason that New York became the center of modern art is that most of the artists had moved here to the United States, and Abstract Expressionism was the first wave of that.

Finally, Pop. Art historically, Pop rose out of Abstract Expressionism and a movement called Neo-Dada, both of which were characterized by continued formal experimentation. Neo-Dada, exemplified by Robert Rauschenberg and Jasper Johns, made continuing use of the readymade throughout the 1950s and into the 1960s. Then, enter onto the scene one Andrew Warhola. Famously, Andy Warhol got his start as a fashion illustrator and shop window decorator, and he was also fascinated by the commodity. Rather than continuing the Neo-Dada use of readymades, Warhol's great insight was that the consumer commodity was the most powerful thing in American culture, and that anything could become a commodity by virtue of its position in the modern media environment. This included such actual commodities as Campbell's soup cans, but also people, like Jackie O, Marilyn Monroe, etc. So, the context for Pop becomes America's increasing material prosperity into the 1960s. In a society where the commodity is God, the leading artists begin using the painstaking tools of traditional art making to recreate commodities, simultaneously acknowledging the commodity nature of art and protesting it.

As a postscript, Pop is often considered one of the last of the modern art movements. Minimalism, perhaps the last, was a reaction to Pop's celebration of glossy commodities, instead choosing to showcase the readymade in the form of raw industrial materials like bricks, steel beams, and styrofoam blocks. After that comes the 1970s and the rise of what we know as postmodern philosophy, which posits that the world can no longer be seen in terms of overarching meta-narratives of progress. Art responded in the same way, fragmenting into a whirl of different styles and truth claims, and joining wider societal movements that include feminism, queer rights, rights of the disabled, and others. This is when the primarily White male narrative I have sketched out finally begins to crack a bit, and you start seeing women and people of color more represented among important artists.

Anyway, I hope that helps sketch out the basic contours of twentieth century art. Please let me know if you have any follow-up questions.