There are many types of clefts, but most generally, when one thinks of clefts, what springs to mind are instances of the so-called it-cleft construction in English, such as it's our work that is important or the c'est-cleft in French c'est moi qui suis venu. In English, there are also other types which are known by the unfortunate name of 'pseudo-clefts', such as what is important is our work or our work is what is important. Similarly, there are as many definitions of clefts as there are cleft types. We find Lambrecht's definition particularly encompassing: "A cleft construction is a complex sentence structure consisting of a matrix clause headed by a copula and a relative or relative-like clause whose relativized argument is co-indexed with the predicative argument of the copula. Taken together, the matrix and the relative express a logically simple proposition, which can also be expressed in the form of a single clause without a change in truth conditions." (Lambrecht 2001: 457) Put in a nutshell, what one needs to remember of clefts is that they are biclausal focus constructions. It is precisely this double nature as both specialized focus constructions and biclausal structures what makes clefts interesting for linguistic analysis; still positing challenges for current theories of syntax. In this respect, it is hardly surprising that the linguistic literature on clefts is remarkably vast, but it is mostly a literature focused on English, mainly aimed at disentangling the intricacies of the semantics and pragmatics of the copular predication (for example, Declerck, 1988; Mikkelsen, 2005; den Dikken, 2005; etc.). On the other hand, Lambrecht (1994) is foundational for the study of clefts from the viewpoint of information structure. The proposals in Drubig (2003) and Drubig and Schaffer (2001: 1079) have been important for a typology of cleft syntax. But while monographies on the English it-cleft continue to be published, such as Patten's (2012), our knowledge of clefts remains uncharted territory for the vast majority of lesser-known languages. To increase the body of knowledge to build a cross-linguistically sound typology of clefts, we still need to expand the range of languages and the range of topics to study. Here we follow the pioneer efforts in Hartmann and Venstraa (2013), who include papers on minority languages for the first time in their collection of papers on clefts. This issue pursues a similar goal; that is, explore aspects of cleft structure in lesser-described languages under different theoretical approaches by using natural data. With this idea in mind, this issue contains a collection of 11 articles on cleft structures from a variety of languages whose syntax of focus we know relatively little about. The languages in question are the following:  Two languages from East Asia: Northern Amis (Formosan) and Tagalog  The West Asian languages Eastern Armenian, Western Armenian and Persian 1 All the articles in this Special issue are based on talks given at the workshop 'Clefts and related focus constructions' organized by us and Katharina Haude as part of the LABEX-EFL, Strand 3, GD1 operation "The typology and corpus annotation of information structure and grammatical relations", which took place on 15-16 February 2018 at the Paris-Villejuif CNRS Campus, with the financial support of the Labex EFL. We want to thank all participants of the workshop, speakers and audience alike, for the fruitful discussion, and to the participants who became authors of this collection. We are especially indebted to the many external reviewers who contributed invaluably to this Special issue with their time, knowledge and efforts.