  One of the main objectives of stage IV galaxy surveys is to constrain gravity
on cosmological scales. To this end, it is crucial to make accurate theoretical
predictions in the nonlinear regime of structure formation in order to maximise
the scientific return. This is possible at a relatively low computational cost
thanks to COLA simulations, an approximate and much faster alternative to full
$N$-body simulations. In this thesis, we focus on two modified gravity
theories, $f(R)$ and nDGP, and present an analysis of how COLA simulations can
be combined with empirical models for the galaxy-halo connection to produce
realistic mock galaxy catalogues in modified gravity. We then use the resulting
galaxy catalogues to study the effects of modified gravity and validate COLA
simulations for several probes of the large-scale structure like the galaxy
power spectrum, bispectrum and the void-galaxy cross-correlation function.
Finally, we propose the COLA method for the extension of cosmological emulators
to modified gravity theories and showcase its potential by training an emulator
for the nDGP boost factor of the matter power spectrum, i.e., the ratio of the
power spectrum in nDGP gravity with that in general relativity.
