1) Micro-evolutionary predictions are complicated by ecological feedbacks like density dependence, while ecological predictions can be complicated by evolutionary change. A widely used approach in micro-evolution, quantitative genetics, struggles to incorporate ecological processes into predictive models, while structured population modelling, a tool widely used in ecology, rarely incorporates evolution explicitly. 2) In this paper we develop a flexible, general framework that links quantitative genetics and structured population models. We use the quantitative genetic approach to write down the phenotype as an additive map. We then construct integral projection models for each component of the phenotype. The dynamics of the distribution of the phenotype are generated by combining distributions of each of its components. Population projection models can be formulated on per generation or on shorter time steps. 3) We introduce the framework before developing example models with parameters chosen to exhibit specific dynamics. These models reveal (i) how evolution of a phenotype can cause populations to move from one dynamical regime to another (e.g. from stationarity to cycles), (ii) how additive genetic variances and covariances (the G matrix) are expected to evolve over multiple generations, (iii) how changing heritability with age can maintain additive genetic variation in the face of selection and (iii) life history, population dynamics, phenotypic characters and parameters in ecological models will change as adaptation occurs. 4) Our approach unifies population ecology and evolutionary biology providing a framework allowing a very wide range of questions to be addressed. The next step is to apply the approach to a variety of laboratory and field systems. Once this is done we will have a much deeper understanding of eco-evolutionary dynamics and feedbacks.