This paper reports progress in developing a computer model of language acquisition in the form of (1) a generative grammar that is (2) algorithmically learnable from realistic corpus data, (3) viable in its large-scale quantitative performance and (4) psychologically real. First, we describe new algorithmic methods for unsupervised learning of generative grammars from raw CHILDES data and give an account of the generative performance of the acquired grammars. Next, we summarize findings from recent longitudinal and experimental work that suggests how certain statistically prominent structural properties of child-directed speech may facilitate language acquisition. We then present a series of new analyses of CHILDES data indicating that the desired properties are indeed present in realistic child-directed speech corpora. Finally, we suggest how our computational results, behavioral findings, and corpus-based insights can be integrated into a next-generation model aimed at meeting the four requirements of our modeling framework.