We present results of a theoretical study of a prototypical weak ferromagnet ZrZn2. We use the density-functional theory (DFT)+dynamical mean-field theory (DMFT) method to study the electronic and local magnetic properties. The obtained DFT+DMFT electronic self-energies are Fermi-liquid-like, indicating a small effective mass enhancement of the Zr 4d states m∗/m∼1.1-1.3 accompanied by partly formed local moments within the electronic states of t2g symmetry. The effect of electronic interaction is shown to be essential for determining the correct topology of some of the Fermi surface sheets. To study in detail the pressure dependence of the Curie temperature TC and corresponding pressure-induced quantum phase transition, we consider an effective single-band model, constructed using the Zr 4d contribution to the total density of states. The model is studied within static and dynamic mean-field theory, as well as spin-fermion approach. We show that the spin-fermion approach yields the temperature dependence of susceptibility at ambient pressure and the pressure dependence TC(p), including the first-order quantum phase transition at p≈1.7 GPa, comparable well with the experimental data.