Eshetu has been featured in solo and group exhibitions at prestigious institutions such as Tate Britain, DAADgalerie in Berlin, the Smithsonian National Museum of African Art, the Metropolitan Museum of Art, the Museum of Modern Art, Haus der Kulturen der Welt, Mudec Museo Delle Culture Milano, the Humboldt Forum, the National Gallery of South Africa, the Baltimore Museum of Art, the Institute of Contemporary Arts in London, the Musée des beaux-arts de Montréal, the Studio Museum, the Stedelijk Museum, Museo Tamayo Arte Contemporáneo, the Guangdong Museum of Art, and others. He has also participated in the 54th Venice Biennale, the 10th Sharjah Biennial, the 13th Gwangju Biennale, the 11th Shanghai Biennale, the 8th Göteborg International Biennial for Contemporary Art, the Dak’Art Biennial, and documenta 14. Additionally, his work has been showcased at several video festivals, including multiple editions of the Venice Film Festival and others across Europe, Africa, Asia, and the Americas. His works are in the collections of the Smithsonian Institution, the Museum of Modern Art, Tate Britain, the Metropolitan Museum of Art, the Museo delle Civiltà, the Gwangju Biennale Foundation, and MACRO Museo D’arte Contemporanea, among others.

He has received numerous residencies and fellowships, most recently at the Victoria & Albert Museum in London (2023), a fellowship at the Smithsonian Institution in Washington, D.C. (2022), a residency at the Tarabya Cultural Academy in Istanbul (2016/17), and at the DAAD Berliner Künstlerprogramm (2012). He has also been awarded various prizes and recognitions at video festivals around the world, including the Verona Film Meeting (2005), the Asolo Film Festival (2002), and the International African Film Festival (1999).