Bose-Hubbard models capture physics of cold atoms in optical lattices. Despite their simplicity, they are not exactly analytically solvable in any dimension. In the first part of the talk, I will discuss basic properties of the 1D Bose-Hubbard model focusing on physically meaningful observables such as the ground state energy, the variance of on-site atom number occupation, and the nearest-neighbor correlation function. I will present analytical results coming from very high-order perturbative expansions and carefully compare them to numerical simulations. In the second part of the talk, I will show how the position of the critical point of the 2D Bose-Hubbard model can be efficiently obtained from the variance of on-site atom number occupation and the nearest-neighbor correlation function. The analogies between the experimental studies of the lambda transition in liquid helium-4 and our theoretical studies of the superfluid-Mott insulator transition of the 2D Bose-Hubbard model will be discussed.