Importance of repulsive interactions for the equation of state and other properties of strongly interacting matter

We illustrate the role of repulsive interactions in a hadron-resonance gas at freeze-out and in a gas of quark-gluon bags. Taking into account non-zero size of particles in hadron gas leads to a significant decrease and shift of the net-baryon density maximum. The transition point from baryon to meson dominated matter depends on the difference between baryon and meson radii. We also show that depending on the properties of the quark-gluon bags one may obtain any type of the phase transition from hadron gas to quark-gluon plasma: the first or second order, as well as four types of the crossover.