A detailed low-temperature treatment of the domain wall or interface pinning by imperfections in disordered systems with discrete symmetry of the order parameter is presented. Crossover behavior as well as analogies between pinning mechanisms in different systems is analyzed. Pinning may arise from random bonds, when the disordering agents do not break the local symmetry of the order parameter, or from random fields, when the disordering agents do break this symmetry. The interface roughness and response to an external driving force are discussed. The model is explained for dilute magnetic systems in a uniform field where the magnetic domain walls are pinned by random fields and/or random bonds. The results are, however, more general and apply also to interfaces in other systems, e.g., in fluid-fluid interfaces, (anti)ferroelectrics, solitons in incommensurate systems, etc. The interface roughness and pinning pressure (force per unit area) are estimated for weak and strong pinning and their scaling relations to length scale, temperature, frequency, and disorder strength (concentration) are given. The interface contribution to the static and dynamic susceptibility at low temperatures is evaluated. Because of pinning, the low-temperature dynamical susceptibility of disordered ferromagnets in or out of equilibrium carries a [ln(1/\ensuremath{\omega})${]}^{2/\mathrm{\ensuremath{\theta}}}$ frequency dependence in addition to the Debye relaxation behavior. In particular, \ensuremath{\theta}=(d+1)/3 for random-field systems, and \ensuremath{\theta}(d=2)=1/3 and \ensuremath{\theta}(d=3)\ensuremath{\approxeq}0.83 for random-bond systems.