We consider a variety of vintage-capital models of a firm's choice of technology under uncertainty in the presence of adjustment costs and technology-specific learning. Similar models have been studied in a deterministic setting. Part of our objective is to examine the robustness of the implications of the certainty models to uncertainty. Our analysis highlights the role of the specification of costs of adjustment: if an adjustment cost comes only in terms of accumulated technology-specific expertise (cf. Parente (1994)), we prove that the implications are robust for a variety of specifications of the firm's production function, however, once a cost paid in units of the produced good is introduced, predictions of an uncertainty model become increasingly different as uncertainty increases. Tractability of our models allows us to disentangle the effects of the models' assumptions, provide characterization of optimal policies, demonstrate the impact of uncertainty on the frequency of technology adoptions and growth in the economy, and present comparative statics.