Recursion, understood as a fundamental feature of natural languages, does not occur uniformly at all linguistic levels. Moreover, there are important cross-linguistic differences as to the extent to which recursive structures are allowed at a given level. A good example for this is compounding. When considering a set of two languages that have compounding as a means of enlarging their lexicons, it may well be the case that one of them resorts to this word-formation process recursively, whereas the other is reluctant to construct compounds consisting of more than two simple immediate constituents.In recent years, several proposals have been made to account for such differences. A quick glance at these proposals reveals as possible reasons for the lack of recursion: left-headedness, word-stress rules, (absence of) linking elements, parsing problems, and semantic constraints. Unfortunately, many relevant contributions to this topic display a blatant gap between strong explanatory ambition and insufficient empirical foundation. In other words, restrictions effective in a limited set of languages are often claimed to exist in many other languages and are presented as (potential) universals.The present paper gives an overview of the possibilities and constraints concerning recursion in N-N compounds, which represent the most representative type of compounds in many languages. Its aim is to evaluate the well-foundedness of recent contributions to the topic, with data coming primarily from Indo-European languages (especially Germanic, Romance, Greek and Slavonic) as well as Hungarian, Japanese and Turkish. It advocates for a holistic approach, wherein the (non-)availability of recursive compounds must not be considered isolated from other means of depicting stable concepts in a language. Naturally, all conclusions must remain provisional as only a small sample of the world's languages is under scrutiny.