The search-and-matching model of the labor market fails to match two important business cycle facts: (i) a high volatility of unemployment relative to labor productivity, and (ii) a mild correlation between these two variables. We address these shortcomings by focusing on technological learning-by-doing: the notion that it takes workers' time using a technology before reaching their full productive potential with it. We consider a novel source of business cycles, namely, fluctuations in the speed of technological learning, and show that a search-and-matching model featuring such shocks can account for both facts. Moreover, our model provides a new interpretation of recently discussed news shocks.