This dissertation analyzes the perception of endlessness in digital media from the 1970s to today, a characteristic which I argue is unique to live, networked screens and is deeply imbricated with the rise of platform capitalism. Digital media have frequently been characterized as boundless, as a continual, almost elemental, stream of images and information. From claims of “information overload” in the 1970s, to the cloud metaphors used today, networked media have been understood and experienced as expansive and without limits. This dissertation traces the history of this tendency, focusing on what I term the “infinite aesthetic” of digital media. The infinite aesthetic can be found in the infinite scroll of social media feeds and search results, in the loops of a GIF and the proliferation of a meme, in the auto play function of a streaming platform and the background animations of a video game. These new never-ending moving images accompany the rise of 24/7 networks and the neoliberal workplace, and the yoking of mobile computing with the attention economy. This dissertation traces four major case studies that represent the emergence of infinite images as an emblematic genre of the digital age, and how they relate directly to transformations wrought by post-Fordist capitalism. I argue that the centrality of this aesthetic underpins how the culture of twenty-first century platform capitalism came to be perceived as not only an endless, frictionless flow, but one characterized by exponential growth.This history began in the late 1960s with a little-known experimental video art lab in the Bay Area where artist’s investigations into the new electronic medium of video pioneered the possibilities of an ever-renewing, live image. In this first chapter, “A Counterfeit Infinity: Video Art and Real-Time Aesthetics,” I show how these innovations in the aesthetics of the live video feed were key to the transformation of computers from calculating machines into interactive visual media devices. In the second chapter, “Without Limits: the Animated Screensaver and 24/7 Computing,” I trace the development of the infinite aesthetic to a new genre of moving images - the animated screensaver - which I argue played a central role in the shift to “always on” computing. I analyze how the screensaver’s infinite aesthetic becomes aligned with neoliberal notions of productivity by supporting the practice of leaving the personal computer on at all times. The third chapter, “Without End: The Infinite Scroll and Platform Capitalism,” turns to the history of the “infinite scroll,” which has its roots in the nineteenth-century stock ticker – a historical connection that underscores the imbrication of live, continually unfolding media and the temporal demands of late capitalism. Finally, “Cryptic Futures: The Endless Deferrals of Web3” examines the recent emergence of crypto art and NFT trading as emblematic of the intensification of speculation and the normalization of indebtedness under post-Fordist capitalism. To the endless work time and endless attention mining of the last thirty years of internet culture, we can now add the endless deferral of the future that arises from the perpetual states of indebtedness that fuel finance capitalism.