I am going to discuss recent results of the replica approach to statistical mechanics of a single classical particle placed in a random Gaussian landscape. The particular attention will be paid to the case of landscapes with logarithmically growing correlations and to its recent multiscale generalisations. Those landscapes give rise to a rich multifractal spatial structure of the associated Boltzmann-Gibbs measure. In the limit of large spatial dimension the free energy of the model is shown to reproduce exactly the most general version of Derrida's Generalized Random Energy Model. If time allows, I will briefly mention also the case of a random landscape constructed locally by adding many squared Gaussian-distributed terms, as well as related results on counting stationary points of random Gaussian surfaces.