The presentation is focused on the structure population models in the space of measures. We take a close look at the space of Radon measures equipped with a flat metric and justify why it is an accurate space for considering problems coming from population dynamics. This part of the presentation contains, among the others, an explanation of the Wassestein and flat distances, its mathematical properties and several examples, which show how convenient the proposed setting is. Further, we present and briefly discuss recent results concerning a well posedness and stability of solutions to some particular examples of structured population models. Finally, we describe a new numerical scheme, which is a variation of the commonly used in biology Escalator Boxcar Train method (EBT method) and provide its rate of convergence.