The authors study the junction conditions which have to be satisfied by the various fields at an arbitrary singular hypersurface separating two different spacetimes in scalar-tensor theories of gravity. This work generalizes previous descriptions of thin shells in the Brans-Dicke theory in the sense that a general algorithm, which can be applied to a singular hypersurface of any type (timelike, spacelike or lightlike), is presented, and the possibility of having discontinuous gauge fields is considered. The results obtained in the timelike case apply to arbitrary surface layers and, in particular, to domain walls with, eventually, surface currents as may be the case for some superconducting domain walls coming from a supersymmetric action. The less considered spacelike case might, for instance, correspond to a transition layer, which suddenly appears and disappears, all over space at a given time. The lightlike case has interesting properties because it can at the same time describe a lightlike shell with surface energy density and surface stress, and an impulsive gravitational wave, which is accompanied by shock waves when discontinuous gauge fields are presented. The various examples illustrating the general formalism are considered. These applications concern spherically symmetric shells, and planar shells and impulsive waves. It is briefly discussed which differences appear in the description of a shell when using dilatonic theories instead of scalar-tensor theories of gravity. Some static spherically symmetric solutions of Brans-Dicke theory are presented.