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While cities have become gradually more vertical and complex over the past century, our methods for conceptualising their characteristics and measuring their forms and functions are still largely based in a horizontal mindset. Recent work has sought to shift urban discourse towards understanding cities according to their volumetric properties. Moving the debate further, this paper approaches volumetric urbanism from a morphological perspective, setting out a research agenda that operationalises the concept as a means of better capturing the morphological characteristics of cities as volumetric entities. First, we deconstruct volumetric urbanism into the five basic building blocks that define volumetric morphologies: density, functional mix, compaction and compression, complex networks and interaction intensity. Next, we propose two methods for capturing the urban volumetrics of cities based on spatial and network interaction and apply them to a hypothetical case and a preliminary study of Hong Kong. We conclude by arguing that a volumetric approach is required to capture the complex form of compressed, multi-layered and highly connected cities. In response, urban morphological and planning discourses must move away from the horizontal analytical mindset, embrace a multi-layered three-dimensional view of cities and place greater emphasis on spatial configurations and network relations by measuring interaction.