This paper deals with the semantics and the syntax of modal constructions from a cross-linguistic perspective. It focuses on the syntactic representation of modal polyfunctionality, usually understood as the semantic alternation between root and epistemic readings. This ambiguity is not an idiosyncratic feature of the Germanic languages, as it is also found in other non-related language families. In this contribution, the empirical base is broadened by discussing the data taken from Hansen and de Haan (2009), which covers all major languages spoken in Europe. I discuss the notion of modal polyfunctionality and give a first account of cross-linguistic morpho-syntactic variation among modal constructions in the languages of Europe. The hypothesis is forwarded that there is cross-linguistic evidence for the syntactic relevance of the distinction between epistemic-root polyfunctionality (EPI-ROOT) and alternations within root modality (ROOT). The relative semantic uniformity of modals contrasts with their structural diversity. It will be shown that modals in the languages of Europe vary with respect to two features: (i) the encoding of the subject and (ii) inflectional categories. It is shown that modal constructions are not restricted to canonical subjects, encoded in the default (nominative) case, but also allow for cases other than nominative, or null subjects. Thus, canonical subject constructions appear to be best suited to fully-fledged EPI-ROOT polyfunctionality, whereas quirky or null subjects tend to be restricted to alternations within the semantic domain ROOT. Categories such as the latter need not be marked on the modal itself, but can be assigned to a lexical verb or the copula – a fact which provides evidence for the claim that polyfunctionality is not restricted to ‘modal verbal status’. In the second part of the paper, the following question will be addressed: Which syntactic features are cross-linguistically connected to polyfunctionality? These chapters focus on (a) the distinction between verbs and auxiliaries in modal constructions, (b) raising vs. control status on the modal, and, (c) the coherence of modal verbal complexes. The subsequent analysis presents clear evidence for the tendency towards a loss of inflectional categories, but, on the other hand, does not lend itself to corroboration of the claim that modals form a syntactic category sui generis (cf. Reis 2001). The conclusion is drawn that the distinction raising vs. control is best suited to explain the syntactic prerequisites of polyfunctionality. It will be argued that modals with canonical subjects displaying full EPI-ROOT involve a raising structure, whereas modals with non-canonically case marked subjects displaying only ROOT alternations form control constructions (cf. Abraham 1989, 2001, 2002 on modals in Germanic).