Despite a century of effort, our understanding of how cities evolve is still woefully inadequate. Recent research, however, suggests that cities are complex systems that mainly grow from the bottom up, their size and shape following well-defined scaling laws that result from intense competition for space. An integrated theory of how cities evolve, linking urban economics and transportation behavior to developments in network science, allometric growth, and fractal geometry, is being slowly developed. This science provides new insights into the resource limits facing cities in terms of the meaning of density, compactness, and sprawl, and related questions of sustainability. It has the potential to enrich current approaches to city planning and replace traditional top-down strategies with realistic city plans that benefit all city dwellers.