The conceptualisation of urban systems is a crucial step in their assessment. It not only involves identifying the constituent parts of an urban system, but also directly influences the definition of appropriate measurement tools, evaluation criteria, and stakeholders for the assessment. Choices related to conceptualisation therefore have strong normative implications. Hence, there is a need to develop ways to analyse and compare different approaches in terms of their relative emphases, strengths, and weaknesses. The purpose of this chapter is to respond to this need by developing analytical tools that build on four contrasting metaphors commonly used for describing cities. The set of four metaphors (machine, organism, network, and melting pot) used for this purpose were selected based their ability to capture different existing scientific perspectives on cities. Through elaborating the implications that each of the four metaphors carries for the different aspects of an urban system, our work produced two frameworks, one for analysing approaches to conceptualising urban systems in general, and another directed more specifically at analysing approaches to the assessment of urban systems. In addition to their analytical functions, these frameworks can also provide the language that enables communication between different scientific approaches to urban systems.