In 1975, Grice introduced the notion of implicature, arguing that it was more appropriate to account for a class of apparent lexical ambiguities through pragmatic processes than by multiplying lexical meanings (Modified Ockham's razor: Do not multiply meanings beyond necessity; Grice, 1975). For the past 20 years, experimental approaches have superseded purely theoretical ones, with mixed results. Paradigms using verification tasks on infelicitous sentences, with rate of pragmatic answers and reaction time as measures, have generally concluded in favor of the post-Gricean views (Bott and Noveck, 2004; Noveck and Reboul, 2008). However, some recent studies discuss additional factors affecting implicature processing and have introduced new paradigms which suggest a different conclusion (Katsos and Bishop, 2011; Breheny et al., 2013; Degen and Tanenhaus, 2015; Foppolo and Marelli, 2017; Bill et al.; Jasbi et al.; Sikos et al.). In addition, current research has shown that lexical scales may play a role in the process in keeping with neo-Gricean views. This Frontiers topic is a collection of 12 contributions in experimental pragmatics focusing on different aspects of child and adult processing of implicatures, factors affecting their rate, relevance of testing paradigms, scale diversity, cross-linguistic differences, and variation in triggers.