The new generation of Simpop models presented in this book, as well as the approach followed all along their construction and evaluation, has specifically targeted and tackled the equifinality challenge of (urban) modelling. It is presented as a progression from solving elementary generative problems to adapting models for encompassing a variety of urban situations by sharing open tools.The first chapter presents our empirical knowledge of systems of cities, and ways of summarizing their regular properties. It builds the ‘system of reference’ upon which model-building can take place. Indeed, by generalizing processes and structural properties of empirical case studies in different spatio-temporal contexts, it specifies the elements that can be forecasted (the total urban growth, the degree of differentiation of city sizes, the spatial balance of growth, etc.) and ways to do it (theories of innovation diffusion, of agglomeration economies, of spatial distribution, etc.). By asking ‘is urban future predictable’, we question the logics of urban evolution as well as the different levels of uncertainty attached to different aspects of urban growth and interactions. Identifying the possibility of prediction makes the task of modelling interesting. Identifying key features of systems of cities provides a stylized empirical ground to evaluate simulations and study alternative trajectories. Finally, identifying areas of uncertainty as leading to the processes responsible for the urban evolution calls for a multi-modelling approach that tackles equifinality in the virtual laboratory.The second chapter addresses the first step of the modelling of system of cities. It presents a parsimonious model of the emergence of cities from a homogenous settlement system. It aims to answer a very basic question: are we able to identify a simple set of meaningful mechanisms that reproduces the observed emergence of cities at the scale of thousands of years? The SimpopLocal model is an answer to this question and it raises the challenge of calibration, in order to prove that there exists a set of parameters that are sufficient to model this emergence. It also raises the challenge of formalizing what a good simulation is in terms of long-term urban evolution, in order to automate the search for this parameter set (for which there exists no empirical ways of determination).The third chapter goes beyond the possibility of finding one way of simulating the emergence of cities. It presents a new method for assessing parameter sensitivity, by looking at the necessity of each mechanism within a given model structure. Indeed, despite the diversity of solutions to the calibration challenge, are some parameters isolated, not interacting with other parameters in the simulated output? Are they all necessary, besides being sufficient? A new method called ‘calibration profiling’ was developed to validate not only sufficiency of modelled mechanisms but also the necessity of theoretical hypotheses that are behind the construction of the model. It is a progress of social sciences towards the scientific methods (all things being equal), and it allows to increase the parsimony of urban models.The fourth chapter builds on this quest for parsimony, as it presents an incremental model-building approach to simulate empirical systems of cities. Given the specificity of the system we aim to model, we expect the mechanisms needed to reproduce the observed trajectory to be multiple and interacting in a complex way. Therefore, we have built a framework of hypothesis-testing and implemented modules of mechanisms that we combine and simulate. The combination follows a path of complexification as well as particularisation from any system of cities to a specific case study. The quality of each simulation is evaluated with respect to the populations observed in the corresponding empirical cities. This approach was developed to model the evolution of Soviet and post-Soviet cities from the 1960s on. Its strength is to be transferable at a very low cost to any other national system. A tentative check was performed on Indian cities. We finally show in this chapter that a theoretical-based modular model allows to evaluate and compare the power of different hypotheses to explain urban growth at different periods of time and in different geographical contexts, and therefore suggests a way to account for equifinality in urban models.The fifth chapter corresponds to an innovative way of exploring simulation models, and especially urban models. It considers a parsimonious structure of mechanisms and looks for the diversity of possible outcomes that the model can reach within a reasonable range of parameters. This means that it explores what the trajectory of a system of cities could have been, if we simulate past trends, or what it could be in the future, in terms of two or three properties of the system (like its total population, or the degree of inequality of city sizes). We present the algorithm developed to maximize the diversity of a model’s output, as well as the kind of knowledge it leads to in an empirical context. For instance, we analyze the alternative pasts of the Soviet system of cities (as modelled within different model structures) and the corresponding parameters and their meaning. In particular, we highlight configurations that result in population growth and configurations that result in population shrinkage, configurations that result in hierarchization or in the equalization of city sizes for each of the demographic regimes at two periods of time (Soviet and post-Soviet eras).In the last chapter, we present the platform that brings together and enables all the cutting-edge exploration methods in urban simulation. This integrated, innovative and open toolbox for urban modelling is called OpenMOLE.As an epilogue, we present what could be a world atlas of urban models for global prospective on urban future. We also stress the challenges that hamper its construction so far, especially because of the data challenge that is comparing cities over time and over space. Indeed, each country having (or having not) developed its own way of defining cities and quantifying urban features, there remains a monumental amount of work to collect and harmonize urban data over large period of time, as well as to identify what in each national evolution relates to generic and specific processes. Cumulative modelling could help perform this task, or at least to highlight areas of uncertainties. Our guess is that it will only be achieved by a large collective and interdisciplinary collaboration (between urban and regional specialists, modellers, computer scientists, empirical and theoretical experts, data providers and data analysts) based on open practices (as to data, methods and models).