The structural and vibrational properties of bismuth selenide (Bi${}_{2}$Se${}_{3}$) have been studied by means of x-ray diffraction and Raman scattering measurements up to 20 and 30 GPa, respectively. The measurements have been complemented with ab initio total-energy and lattice dynamics calculations. Our experimental results evidence a phase transition from the low-pressure rhombohedral ($R$-3$m$) phase (\ensuremath{\alpha}-Bi${}_{2}$Se${}_{3}$) with sixfold coordination for Bi to a monoclinic $C$2/$m$ structure (\ensuremath{\beta}-Bi${}_{2}$Se${}_{3}$) with sevenfold coordination for Bi above 10 GPa. The equation of state and the pressure dependence of the lattice parameters and volume of \ensuremath{\alpha} and \ensuremath{\beta} phases of Bi${}_{2}$Se${}_{3}$ are reported. Furthermore, the presence of a pressure-induced electronic topological phase transition in \ensuremath{\alpha}-Bi${}_{2}$Se${}_{3}$ is discussed. Raman measurements evidence that Bi${}_{2}$Se${}_{3}$ undergoes two additional phase transitions around 20 and 28 GPa, likely toward a monoclinic $C$2/$c$ and a disordered body-centered cubic structure with 8-fold and 9- or 10-fold coordination, respectively. These two high-pressure structures are the same as those recently found at high pressures in Bi${}_{2}$Te${}_{3}$ and Sb${}_{2}$Te${}_{3}$. On pressure release, Bi${}_{2}$Se${}_{3}$ reverts to the original rhombohedral phase after considerable hysteresis. Symmetries, frequencies, and pressure coefficients of the Raman and infrared modes in the different phases are reported and discussed.