The earliest known vascular plant reproductive structures were simple, consisting of spore-producing sporangia. In contrast, living lineages may produce complex structures, like flowers, that have many intricately arranged parts. Although the maximum complexity of plant reproductive structures has clearly increased over time, understanding exactly how, when, and why complexity has changed is challenging because plant groups produce disparate reproductive structures that are difficult to compare. Here we quantify changes in reproductive complexity across vascular plants using two simple aspects that can be applied to any lineage: the total number of part types, or geometrically distinct morphological elements, and the degree to which these part types are repeated. We ask how the number and arrangement of part types has changed over time in aggregate and in lineages with different reproductive biology. We find that increases in complexity have not gradually accrued over plant evolutionary history, but are associated with two major pulses. There was an initial rise in maximum complexity from the Late Silurian to the Late Devonian, as multiple lineages evolved a basic set of structures supporting and protecting sporangia. We then see a plateau or a very gradual rise in maximum part number through the Early Cretaceous which reflects diversification of gymnosperm ovulate structures. Lastly, we see a second major increase in complexity over the middle Cretaceous due to the appearance of derived angiosperm clades. Within this overarching pattern, complexity is generally associated with functional diversity; reproductive structures with simple functional roles, such as wind dispersal of spores or pollen, have relatively few parts and show few changes over time. Seed plant ovulate structures, which perform a greater variety of functional roles, generally have more parts and exhibit a general increase in complexity through time. Plants also show a basic tendency for reproductive functions to be transferred away from fertile organs and onto surrounding sterile organs, whose specialization then underlies the specific patterns of complexity that we identify here. The extent to which this process occurs, however, is determined by the overall functional diversity of the reproductive structures, resulting in different patterns in morphological complexity across plant lineages.