Book excerpt: Active matter, i.e. nonequilibrium systems composed of many particles capable of exploiting the energy present in their environment in order to produce systematic motion, has attracted much attention from the statistical mechanics and soft matter communities in the past decades. Active systems indeed cover a large variety of examples that range from biological to granular. This Ph.D. focusses on the study of minimal models of dry active matter (when the fluid surrounding particles is neglected), such as the Vicsek model: point-like particles moving at constant speed and aligning their velocities with those of their neighbors locally in presence of noise, that defines a nonequilibrium universalilty class for the transition to collective motion. Four current issues have been addressed: The definition of a new universality class of dry active matter with polar alignment and apolar motion, showing a continuous transition to quasilong-range polar order with continuously varying exponents, analogous to the equilibrium XY model, but that does not belong to the Kosterlitz-Thouless universality class. Then, the study of the faithfulness of kinetic theories for simple Vicsek-style models and their comparison with results obtained at the microscopic and hydrodynamic levels. Follows a quantitative assessment of Toner and Tu theory, which has allowed to compute the exponents characterizing fluctuations in the flocking phase of the Vicsek model, from large scale numerical simulations of the microscopic dynamics. Finally, the establishment of a formalism allowing for the derivation of hydrodynamic field theories for dry active matter models in three dimensions, and their study at the linear level.