We investigate two examples of models of populations with structure. These are different in character, with the common theme that the structure has an important influence on population outcomes. In the first part we consider a model of kleptoparasitism, the stealing of food from one animal by another. We investigate a model where individuals are allowed to fight in groups of more than two, as often occurs in real populations, but which has not featured in previous theoretical models. We find the equilibrium distribution of the population amongst various behavioural states, conditional upon the strategies played and environmental parameters, and then find evolutionarily stable strategies (ESSs) for the challenging behaviour of the participants. We show that ESSs can only come from a restricted subset of the possible strategies and that there is always at least one ESS. We show that there can be multiple ESSs, and indeed that the number of ESSs is unbounded. Finally we discuss the biological circumstances when particular ESSs occur in terms of key parameters such as the availability of food and the cost of fighting. The second part of the talk concerns the study of evolutionary dynamics on populations with some non-homogeneous structure, a topic in which there is a rapidly growing interest. We investigate the case of non-directed equally weighted graphs and find solutions for the fixation probability of a single mutant in two classes of simple graphs. This process is a Markov chain and we prove several mathematical results. For example we prove that for all but a restricted set of graphs, (almost) all states are accessible from the possible initial states. We then consider graphs within this restricted set or with considerable symmetry. To find the fixation probability of a line graph we relate this to a two-dimensional random walk which is not spatially homogeneous. We investigate our solutions numerically and find that for mutants with fitness greater than the resident, the existence of population structure helps the spread of the mutants. Thus it may be that models assuming well-mixed populations consistently underestimate the rate of evolutionary change.