This paper addresses the effects of solid boundaries on the evolution of two-dimensional turbulence in a finite square domain, for the cases of both decaying and continuously forced flow. Laboratory experiments and numerical flow simulations have revealed the crucial role of the solid no-slip walls as sources of vorticity filaments, which may significantly affect the flow evolution in the interior. In addition, the walls generally provide normal and tangential stresses that may exert a net torque on the fluid, which can change the total angular momentum of the contained fluid. For the case of decaying turbulence this is observed in so-called ‘spontaneous spin-up’, i.e. a significant increase of the total angular momentum, corresponding to a large domain-filling circulation cell in the organized ‘final’ state. For the case of moderate forcing this phenomenon may still be observed, although the filamentary vortex structures advected away from the walls may cause erosion and possibly a total destruction of the central cell. This disordered stage – characterized by a significantly decreased total angular momentum – is usually followed by a re-organization into a large circulation cell (in either the same or opposite direction) with an increased total angular momentum. The scaling behaviour of vorticity structure functions and the probability distribution function of vorticity increments have been investigated for forced turbulence and indicate a strong anisotropy of the turbulent flow in the range of Reynolds numbers considered.