We explore the stability and dynamics of dark–bright (DB) solitons in two-component elongated Bose–Einstein condensates by developing effective one-dimensional vector equations and solving the three-dimensional Gross–Pitaevskii equations. A strong dependence of the oscillation frequency and of the stability of the DB soliton on the atom number of its components is found; importantly, the wave may become dynamically unstable even in the 1D regime. As the atom number in the dark-soliton-supporting component is further increased, spontaneous symmetry breaking leads to oscillatory dynamics in the transverse degrees of freedom. Moreover, the interactions of two DB solitons are investigated with an emphasis on the importance of their relative phases. Experimental results showcasing multiple DB soliton oscillations and a DB–DB collision in a Bose–Einstein condensate consisting of two hyperfine states of 87Rb confined in an elongated optical dipole trap are presented.