This special issue comprises a selection of studies on the acquisition of tense, aspect and modality (TAM) in second languages (L2) which aim to gain insight into the acquiring and learning of TAM representations, as this is one of the most challenging tasks for second language learners (Comajoan, 2014).The seven articles are based on talks presented at the 3rd edition of TAML2 (Tense, Aspect and Modality in a Second Language) in Leiden, The Netherlands which brought together researchers working on different aspects of the acquisition, learning and teaching of TAM in second languages. The papers cover research on (a) aspectual, temporal and modal representations in an L2; (b) pedagogical implications of TAML2 research findings; (c) methodological issues; and (d) contributions to theory building. These research topics are a reflection of a widely recognized need for an updated knowledge base and for innovative methodological tools in the study of temporal, aspectual and modal representations in a second language (see McManus, Vanek, Leclercq, &Roberts, 2017 andSalaberry, 2018).The first article by Verkuyl argues that the Lexical Aspect Hypothesis (Andersen, 1986), which to date still dominates a great part of TAML2 studies, suffers from being based on naïve physics assumed by language philosophers and needs to be reevaluated. Due to their understanding of aspect, a verb has been taken as a predicate rather than as a linguistic unit with its own lexical meaning. This article puts forward the need of understanding the availability of the verb to accept a wide variety of arguments.González and Diaubalick's pilot study on the understudied language combination Dutch-Spanish highlights the importance of methodological questions in TAM research: only in certain experiments, an L1-effect was revealed. Especially due to the high complexity of TAM features, such task effects are not unknown (see Domínguez, Tracy-Ventura, Arche, Michell, & Myles, 2013). The findings of this paper, however, show possible interactions between these effects and a learner's L1. Only by taking all results together, a tendency to overgeneralize the Imperfect was visible. Interestingly, this contrasts to findings on English-speaking