This thesis is concerned with modelling ways in which humans combine and modify concepts. We develop a framework for the hierarchical composition of vague concepts, based on random set theory, prototype theory, and embedded within conceptual spaces. We call this the Hierarchical Conceptual Spaces (HCS) framework. The framework allows for the construction of concepts at varying levels of complexity. We relate the HCS framework to models in the literature, arguing that we can account for key aspects of human concept use in a systematic and grounded way. In particular, we show that the characterisation of concepts as weighted sums of attributes may be accommodated as a special case of the HCS framework under specific conditions. We use the idea of necessity from possibility theory to characterise the weight of each attribute. We then go on to apply the HCS framework in order to model data on human concept use from the psychological literature. We find that there is at least some support for the HCS framework in modelling human concept use. We further investigate an alternative type of compositionality, that of linguistic hedges. We derive a model of linguistic hedges that is semantically grounded, in which hedges are formed by considering the dependence of the threshold of a hedged concept on the threshold of the original concept. We give a basic model and two generalisations, show that the models can be composed and investigate the behaviour in the limit of composition. We compare our results to those in the literature and show that key models from the literature can be derived as special cases of our model. As a further application of our theory, we instantiate each of the HCS model and the linguistic hedges model within a multi-agent system. We show that within the HCS model, shared combination weights emerge, and that properties of these weights may be predicted from the distribution of elements in the conceptual space. We model the use of hedged assertions in a multi-agent simulation of concept development, finding that using contraction hedges like 'very' gives better convergence to shared concepts over time, and that using expansion hedges such as 'quite' reduces concept overlap. However, both these improvements come at a cost of slower speed of convergence. We finally discuss the results we have presented and give suggestions for future work.