Searches for new vector-like quarks at the LHC by both ATLAS and CMS have set mass bounds above the TeV. These searches, however, usually rely on a set of assumptions about the properties of such quarks. After discussing these assumptions, I will show how it is possible to explore different scenarios by relaxing some of them. I will focus in particular on vector-like quarks with large width, on the role of NLO corrections for single production, and on the possibility that vector-like quarks decay into new scalar exotic states.