Drawing with eyes closed and other non-visual art practices in the late 20th – early 21st centuries clearly resonate with the avant-garde critique of rational vision and the post-war tradition of overcoming collective trauma. Being affected by current personal or geopolitical events, contemporary artists are often ready to close their eyes. This paper aims at tracing the origins of non-visual techniques in the art of the early 21st century, as well as at comparing them with the methods of the Dada, Surrealists, Futurists, and other experiment groups of the early 20th century. Let us trace how drawing reveals a connection with tactility and bodily interaction in different periods, how blind and automatic drawing becomes a method of exploring a non-obvious, deferred meaning. These practices allow multiple interpretations of the art work and such polysemy becomes a part of the artistic statement — there can be no certainty about what exactly we see and how we relate to it. The article provides examples of different artistic strategies for using blindness as a creative method in the late 20th – early 21st centuries, when rethinking of traditional creative techniques, among other things, leads to the rejection of visual control and dominance of one sensory channel.