Motivated by recent interest in their applications, we report a systematic study of Cs atomic properties calculated by a high-precision relativistic all-order method. Excitation energies, reduced matrix elements, transition rates, and lifetimes are determined for levels with principal quantum numbers n <= 12 and orbital angular momentum quantum numbers l <= 3. Recommended values and estimates of uncertainties are provided for a number of electric-dipole transitions and the electric dipole polarizabilities of the ns, np, and nd states. We also report a calculation of the electric quadrupole polarizability of the ground state. We display the dynamic polarizabilities of the 6s and 7p states for optical wavelengths between 1160 and 1800 nm and identify corresponding magic wavelengths for the 6s - 7p(1/2) and 6s - 7p(3/2) transitions. The values of relevant matrix elements needed for polarizability calculations at other wavelengths are provided.