In this article we consider the Slavic perfective/imperfective opposition, a well-known example of viewpoint aspect which establishes a classificatory grammatical category by means of stem derivation. Although Slavic languages are not unique in having developed a classificatory aspect system, a survey of such systems shows that the Slavic perfective/imperfective opposition is a particularly rare subcase of such systems, first of all because it combines prefixing with suffixing patterns of derivation. We therefore explore the morphology involved, tracing its development from Proto-Indo-European into Early Slavic. The emergence of Slavic aspect is atypical for grammatical categories, and it deviates considerably from mainstream instances of grammaticalization in many respects. We show that there is a strong tendency (i) towards abandonment of highly lexically conditioned and versatile suffix choices in Proto-Indo-European and in Common Slavic, which led to fewer and more transparent suffixes, and (ii) towards concatenation, away from originally non-concatenative (fusional) schemata. Furthermore, we compare Slavic with some other Indo-European languages and inquire as to why in Europe no other Indo-European group beyond Slavic went so far as to productively exploit newly developed prefixes (or verb particles) merely for use as aspectual modifiers of stems and to combine them with a (partially inherited, partially remodelled) stock of suffixes to yield a classificatory aspect system. The Slavic system, thus, appears quite unique not only from a typological point of view, but also in diachronic-genealogical terms. Based on this background, amplified by some inner-Slavic biases in the productivity of patterns of stem derivation, we pose the provocative question as to whether the rise and consolidation of the stem-derivational perfective/imperfective opposition in Slavic was favoured by direct and indirect contacts with Uralic (Finno-Ugric) and Altaic (Turkic) populations at different periods since at least the time of the Great Migrations.