Abstract Logics of Critical Explanation proposed a methodological approach that could render the insights of Poststructuralist Discourse Theory (PDT) and post-Marxist political theory more conducive to critical empirical research. It also offered a language with which to counter positivist tendencies to colonize the space of methods and research strategies, showing how PDT could facilitate both explanatory and critical endeavours. Since its publication in 2007, a number of studies have applied the logics framework to empirical cases, while critically engaging with its methodological and theoretical arguments. The main purpose of this article is to evaluate some of these developments, and to set out some future challenges faced by this research programme.