Anni Albers, the preeminent twentieth-century weaver, identified the primary aesthetic feature of woven art as the cloth’s texture or “tactile sensibility”—an aesthetic that demands the closest interaction between medium and design.My thesis argues that contemporary artists Lia Cook and Grethe Sørensen create woven textiles using digital handlooms that exemplify Albers’ aesthetic with visual programs firmly rooted in the formal materiality of woven cloth.Digital-loom technology facilitates the rendering of complex weave structures, thus increasing the range of visual and tactile programs that can be expressed in the woven form and the ability to align the visual with the structural form of the textile.This paper explores Albers’ weaving aesthetic and demonstrates how Cook and Sørensen embrace Albers’ tactile sensibility in their work. It includes a detailed analysis of key works by each artist, the visual and tactile program of these works, and how each artist uses digital tools to create woven art that exemplifies Albers’ aesthetic of tactility. I argue that Cook and Sørensen’s success is a function of their skill and expertise in traditional weaving and their ability to seamlessly integrate digital tools into an existing body of material-based craft knowledge. By maintaining an immediate relationship with material and process, Cook and Sørensen use digital technologies to expand the horizons of the traditional woven form and give new life to Albers’ aesthetic. The paper also examines the digital loom as part of a continuum of weaving technologies that spans thousands of years, discusses the transition of digital loom technology from industrial to artistic uses, and provides a history of the invention of the Thread Controller loom and the first digital jacquard handloom, along with an explanation of its functionality.