The influences of phase transitions on Martian mantle convection and melting in the Martian mantle have been studied with an axisymmetric spherical-shell model. An extended Boussinesq model in which viscous and adiabatic heatings are included has been used. There are depth dependences in the thermal expansivity and gravity, which taken together, decrease by a factor of between 2 and 3 across the Martian mantle. The two destabilizing exothermic phase transitions, olivine to β-spinel and β- and γ-spinel transitions, above the Martian core-mantle boundary (CMB) accelerate the mantle flow and result in an amplification and superheating of plumes in Mars. The additional consideration of the endothermic phase transition, spinel to perovskite transition, which was only likely present in the early evolution of the planet, has little influence on Martian mantle convection in this model. Strong localized viscous heating is generated near the CMB and underneath the lithosphere because here the flow bends over sharply. A possible volcanic evolution of Mars can be derived from a comparison of the temperature fields with the solidus of anhydrous peridotite if the cooling of the Martian mantle is taken into account. In the early evolution the mantle was molten to a high degree along the plume axis, which possibly resulted in a strong differentiation of the mantle. As the planet cooled down, the region of melt generation receded to where the maximum of viscous heating occurred: at the CMB and immediately underneath the lithosphere. Upon further cooling, the deep-mantle melt source region became subsolidus. The most recent volcanism on Mars was most likely generated at a shallow depth below the lithosphere.