We present eco-genetic modeling as a flexible tool for exploring the course and rates of multi-trait life-history evolution in natural populations. We build on existing modeling approaches by combining features that facilitate studying the ecological and evolutionary dynamics of realistically structured populations. In particular, the joint consideration of age and size structure enables the analysis of phenotypically plastic populations with more than a single growth trajectory, and ecological feedback is readily included in the form of density dependence and frequency dependence. Stochasticity and life-history trade-offs can also be implemented. Critically, eco-genetic models permit the incorporation of salient genetic detail such as a population's genetic variances and covariances and the corresponding heritabilities, as well as the probabilistic inheritance and phenotypic expression of quantitative traits. These inclusions are crucial for predicting rates of evolutionary change on both contemporary and longer timescales. An eco-genetic model can be tightly coupled with empirical data and therefore may have considerable practical relevance, in terms of generating testable predictions and evaluating alternative management measures. To illustrate the utility of these models, we present as an example an eco-genetic model used to study harvest-induced evolution of multiple traits in Atlantic cod. The predictions of our model (most notably that harvesting induces a genetic reduction in age and size at maturation, an increase or decrease in growth capacity depending on the minimum-length limit, and an increase in reproductive investment) are corroborated by patterns observed in wild populations. The predicted genetic changes occur together with plastic changes that could phenotypically mask the former. Importantly, our analysis predicts that evolutionary changes show little signs of reversal following a harvest moratorium. This illustrates how predictions offered by eco-genetic models can enable and guide evolutionarily sustainable resource management.