We study, from first principles, the pressure exerted by an active fluid of spherical particles on general boundaries in two dimensions. We show that, despite the non-uniform pressure along curved walls, an equation of state is recovered upon a proper spatial averaging. This holds even in the presence of pairwise interactions between particles or when asymmetric walls induce ratchet currents, which are accompanied by spontaneous shear stresses on the walls. For flexible obstacles, the pressure inhomogeneities lead to a modulational instability as well as to the spontaneous motion of short semi-flexible filaments. Finally, we relate the force exerted on objects immersed in active baths to the particle flux they generate around them.Active forces have recently attracted much interest in many different contexts [1]. In biology, they play crucial roles on scales ranging from the microscopic, where they control cell shape and motion [2] to the macroscopic, where they play a dominant role in tissue dynamics [3,4]. More generally, active systems offer novel engineering perspectives, beyond those of equilibrium systems. In particular, boundaries have been shown to be efficient tools for manipulating active particles. Examples range from rectification of bacterial densities [5,6] and optimal delivery of passive cargoes [7] to powering of microscopic gears [8,9]. Further progress, however, requires a predictive theoretical framework which is currently lacking for active systems. To this end, simple settings have been at the core of recent active matter research.Understanding the effect of boundaries on active matter starts with the mechanical pressure exerted by an active fluid on its containing vessel. This question has been recently studied extensively for dry systems [10][11][12][13][14][15][16][17], revealing a surprisingly complex physics. For generic active fluids, the mechanical pressure is not a state variable [13]. The lack of equation of state, through a dependence on the wall details, questions the role of the mechanical pressure in any possible thermodynamic description of active systems [18,19]; it also leads to a richer phenomenology than in passive systems by allowing more general mechanical interplays between fluids and their containers.Interestingly, for the canonical model of self-propelled spheres of constant propelling forces, on which neither walls nor other particles exert torques, the pressure acting on a solid flat wall has been shown to admit an equation of state [11,12,19]. While the physics of this model does not clearly differ from other active systems, showing for instance wall accumulation [20] and motility-induced phase separation [21][22][23], the mechanical pressure exerted on a flat wall satisfies an equation of state, even in the presence of pairwise interactions [11,12,19]. One might thus hope that the intuition built on the rheology of equilibrium fluids extends to this case. Derived in a particular setting, the robustness of this equation of state however remains an open question. For...