Microsimulation aims at mimicking a real population under scrutiny and simulating its temporal and spatial evolution. This thesis proposes first two applications related to actual problems: the creation of a synthetic population of space debris, causing potential damages to functional satellites and the forecast of the health needs of the elderlies for Belgium until 2030. Then, the observed limitations of the methods generate new methodological research questions. Hence, the impact of specific orders of the application of the sub-models for a discrete time simulation with a fixed time-step of a synthetic population is investigated and quantified. Then, we propose the calendar based approach consisting in fixing birthdays for each agent and a date of death for the dying agents. This reduces the variability of the results. These studies about the evolution of synthetic populations induced theoretical questions whose scope goes beyond the presented framework. Indeed, noticing that simulating the occurrence or not of an event is equivalent to perform a binary classification, we delved into the problem of highly unbalanced classes with unobserved variables. These achievements have been obtained by developing and comparing a feedforward neural network and a logit discrete choice model.