Willy Kautz was Chief Curator of the Tamayo Museum (2012-2013), period in which he held the exhibitions: There are more routes than ours, Matt Mullican. That World, and Erick Beltrán. Atlas Eidolon. He was Head of Visual Arts and curator of the Casa del Lago Juan José Arreola (2010-2011); coordinator and curator of Casa Vecina (2010); and associate curator of the Tamayo Museum (2001-2005).

Its main exhibitions include: Quasi-corpus. Concrete and neo-concrete art from Brazil. Tamayo Contemporary Art Museum (2002); Gordon Matta-Clark: Anarchitectonic projects, Museo Tamayo Arte Contemporáneo (2003); Look at Schendel. Amorphous Continuum, Museo Tamayo Arte Contemporáneo (2004); I use perfume to occupy more space, Museo de Arte Carrillo Gil (2009); Poor Rich Artist. The aesthetic value in transaction, Casa del Lago (2012); Tropicalia Negra, Museo Experimental El Eco (2013); José Luis Sánchez Rull, Radioactive Cemetery. Humans kill, meat speaks !, El Chopo University Museum (2014).