The key aim of this special issue is to make developmental theory proposals concrete enough to evaluate with empirical data. With this in mind, I discuss proposals from the "Universal Grammar + statistics" (UG+stats) perspective for learning several morphology and syntax phenomena. I briefly review why UG has traditionally been part of many developmental theories of language, as well as common statistical learning approaches that are part of UG+stats proposals. I then discuss each morphology or syntax phenomenon in turn, giving an overview of relevant UG+stats proposals for that phenomenon, specific predictions made by each proposal, and what we currently know about how those predictions hold up. I conclude by briefly discussing where we seem to be when it comes to how well UG+stats proposals help us understand the development of morphology and syntax knowledge.