Classical statistical mechanics describes the macroscopic properties of large numbers of particles. It has a hidden weakness: it assumes that the microscopic forces derive from a Hamiltonian. The same mathematical object then controls both the equations of motion, and the Boltzmann distribution. This is why quantities like pressure are not only time averages of forces (on a wall), but also thermodynamic state functions (which exist independently of any wall). Active matter systems are different. Their particles take energy out of the environment, and use it for dissipative self-propulsion, violating Hamiltonian dynamics. Examples include swimming micro-organisms, and synthetic colloids propelled by optical or chemical energy. The absence of a Hamiltonian-derived detailed balance principle requires a rebuild of statistical mechanics, with some surprising outcomes. For example: (i) the pressure of an active fluid on a wall is not a state function -- it depends on the type of wall\DSEMIC (ii) various interfacial phenomena, governed in equilibrium by a single surface tension, now involve different tensions, some of which can be negative. I will survey these among other surprises and, if time allows, say how they affect kinetic questions such as nucleation rates.