In recent decades, the world has experienced rates of urban growth unparalleled in any other period of history and this growth is shaping the environment in which an increasing proportion of us live. In this paper, we use a longitudinal dataset from Foursquare, a location-based social network, to analyse urban growth across 100 major cities worldwide. Initially, we explore how urban growth differs in cities across the world. We show that there exists a strong spatial correlation, with nearby pairs of cities more likely to share similar growth profiles than remote pairs of cities. Subsequently, we investigate how growth varies inside cities and demonstrate that, given the existing local density of places, higher-than-expected growth is highly localized while lower-than-expected growth is more diffuse. Finally, we attempt to use the dataset to characterize competition between new and existing venues. By defining a measure based on the change in throughput of a venue before and after the opening of a new nearby venue, we demonstrate which venue types have a positive effect on venues of the same type and which have a negative effect. For example, our analysis confirms the hypothesis that there is large degree of competition between bookstores, in the sense that existing bookstores normally experience a notable drop in footfall after a new bookstore opens nearby. Other place types, such as museums, are shown to have a cooperative effect and their presence fosters higher traffic volumes to nearby places of the same type.