Over the last two decades labor market dynamism, measured by flows of workers between employers, declined substantially in the US. During the same period employment polarized into low and high-skill jobs. This paper shows that the two trends are linked. First, I provide a framework to study employment and worker flows in presence of two-sided heterogeneity. I analyze within this framework the effects of routine-biased technological change and the increasing supply of college graduates on labor market flows. When routine-biased technological change displaces mid-skill jobs, it lowers the opportunity to move up to better jobs for low-skilled workers. Similarly, highly skilled workers have less opportunity to take typical stepping stone jobs and either trade down to lower-skill jobs or start employment higher up the job ladder. The rising share of college graduates puts further pressure on labor markets by increasing competition for jobs from top to bottom. In equilibrium, workers trade down to jobs with lower skill intensity to gain employment but may find it harder to move up as they are competing with more highly educated workers. I quantitatively assess whether such mechanisms contributed to the fall in labor market dynamism, by estimating the model using data on labor market flows. I find that routine-biased technological change accounts for about one-third of the decline in job-to-job mobility for workers without a college degree, while the remaining decline in mobility is mainly driven by a decline in the dispersion of match-specific productivity and its innovation rate.