  There is strong expectation that cities, across time, culture and level of
development, share much in common in terms of their form and function.
Recently, attempts to formalize mathematically these expectations have led to
the hypothesis of urban scaling, namely that certain properties of all cities
change, on average, with their size in predictable scale-invariant ways. The
emergence of these scaling relations depends on a few general properties of
cities as social networks, co-located in space and time, that conceivably apply
to a wide range of human settlements. Here, we discuss the present evidence for
the hypothesis of urban scaling, some of the methodological issues dealing with
proxy measurements and units of analysis and place these findings in the
context of other theories of cities and urban systems. We show that a large
body of evidence about the scaling properties of cities indicates, in analogy
to other complex systems, that they cannot be treated as extensive systems and
discuss the consequences of these results for an emerging statistical theory of
cities.
