Large assemblies of living or synthetic self-propelled particles make up Active Matter. They operate far from equilibrium without necessarily leading to macroscopic currents, hence a superficial resemblance to their equilibrium counterparts. Our project focuses on the theoretical challenges posed by the emergent local and global order observed in such systems. It builds on the counterintuitive idea, supported by encouraging attempts, that thermodynamics-based ideas will help rationalize and predict the wealth of phase behaviors observed in active systems. Our threefold approach is based on exploring statistical concepts like entropy (without its thermal meaning, understood as a means of counting states), exploring mechanical or chemical concepts like pressure, chemical potential, surface tension (without their free energy interpretation), and connecting local structure to effective interactions, by means of energetics or dynamic approaches (without invoking the Boltzmann measure).