The large-scale structure of the universe is the result of the gravitational collapse of small initial density fluctuations. Such process takes place in an expanding universe, whose expansion rate is accelerated by an unknown component called dark energy. Thus, large-scale structure measurements offer a unique window to test the laws of gravity at cosmological scales, while probing the nature of dark energy. This is one of the primary objectives of the ongoing next-generation cosmological surveys, such as the Euclid mission. In my talk I will give an overview of how the required theoretical predictions for the interpretation of these upcoming data can be obtained using numerical simulations in the context of alternative theories of gravity. In particular, I will focus on the virtues of so-called cosmological emulators, which allow us to overcome computational limitations that affect the direct exploration of model parameter space and are the subject of my PhD Thesis.