Modernism in painting spans roughly a century, conventionally traced from Impressionism in the 1870s through to Abstract Expressionism in the mid-twentieth century, and art historians commonly read this whole span as a sustained, escalating argument over what a painting is actually supposed to do. Rather than each movement simply developing a new style for its own sake, successive modernist movements tended to question a specific assumption about painting that the previous movement had left largely unquestioned, pushing the argument another step further each time.
Impressionism questioned whether a painting had to depict a static, idealised scene
Impressionism broke from the academic painting tradition preceding it by treating a fleeting visual impression, captured through loose, visible brushwork and an emphasis on shifting light, as a legitimate subject in itself, rather than requiring a painting to present a carefully composed, idealised, static scene the way academic convention had generally demanded. This questioned one specific assumption, that painting's job was to present a polished, timeless-feeling image, while still largely keeping painting's commitment to representing something recognisable from the visible world.
Later movements kept pushing further, until abstraction dropped representation itself
Movements following Impressionism kept extending this questioning process, each pushing further past an assumption the last movement had still held onto. Where Impressionism still represented recognisable subjects, later movements increasingly questioned whether a painting needed to represent anything visually recognisable at all, eventually arriving at fully abstract painting that abandoned representational subject matter altogether. Abstract Expressionism, generally treated as modernism's culminating movement, pushed this furthest still, treating the physical act of painting itself, gesture, scale and raw material presence, as the painting's actual subject, rather than anything the painting might be understood to depict.
What we're still unsure about
The general chronological sequence of major modernist movements, and their commonly cited stylistic innovations, are well documented, extensively studied art history. What's more genuinely a matter of ongoing art-historical debate is how neatly this "escalating argument" narrative actually describes what was happening at the time, since it's a framework largely constructed with hindsight, and some art historians argue it overstates modernism's internal logical progression while understating the messier, more contingent historical and social factors, patronage, exhibition politics, individual artists' idiosyncratic choices, that also shaped how these movements actually developed.
This sits inside Modernism (Impressionism through Abstract Expressionism), one of seven topics in Art History, one of five domains in Art, one of seventeen subjects the app can quiz you on.