This talk offers a conceptual and empirical overview of the evolving relationship between computer capability and human skill demands. I begin by sketching historical thinking about machine displacement of human labor---which is primarily a series of grim and ultimately incorrect predictions about collapsing employment and excess leisure. I next consider the impact of computerization on industrialized country labor market over the last three decades, which is seen in the phenomenon of labor market "polarization" -- meaning the simultaneous growth of high-education, high-wage and low-education, low-wages jobs. I will finally reflect on how recent advances in artificial intelligence and robotics may shape the trajectory of employment growth, occupational change and skill demands in coming decades. A key observation of the talk is that journalists and expert commentators overstate the extent of machine substitution for human labor and ignore the strong complementarities that increase productivity, raise earnings, and augment demand for skilled labor. The challenges to substituting machines for workers in tasks requiring flexibility, judgment, and common sense remain immense, primarily because humans apply tacit skills and knowledge that have proved extraordinarily difficult to codify. Contemporary computer science seeks to overcome this challenge by building machines that learn from human examples, thus inferring the rules that we tacitly apply but do not explicitly understand.