This paper reviews the research outputs of my recent RIETI projects on the size and spatial patterns of cities and discusses their policy implications. It is a well-known fact that city size distribution follows a power law in many countries. We found that this regularity holds not only at the country level, but also in regions within a country. Specifically, the sizes and spatial patterns of cities exhibit the recursive "central place pattern" in which a large city has many surrounding small cities, from which a spatial fractal structure of cities results. Each part of the fractal consists of cities that exhibit the central place pattern with a city-size distribution following a common power law. Such regularity has important policy implications, as the size of a city is known to correlate with various socio-economic indices such as industrial diversity, household income, and education levels of workers. City growth is strictly subject to this regularity since the size and spatial distributions of cities remain essentially the same. The regional policies must take this persistent regularity as a de facto constraint.