This paper presents an overview of the waves and patterns that are formed when the oscillatory Belousov-Zhabotinsky medium flows through a packed bed reactor. At a sufficiently high flow velocity, this flow-distributed oscillation (FDO) gives rise to stationary waves with constant forcing at the inflow and to traveling waves with periodic forcing at the inflow. The wavelength of the stationary FDO wave is found to depend on flow velocity and on the effective diffusion coefficient (diameter of packing medium). We demonstrate the breakdown of stationary FDO waves at low flow velocity at which the space-periodic structure is replaced by irregular waves. At high flow velocity, periodic boundary forcing is found to give FDO waves that propagate either with a constant or with an oscillatory velocity. The wavelength and the velocity of the constant velocity upstream or downstream propagating waves are found to agree quantitatively with those predicted theoretically. Finally, we investigate the effect of a frequency gradient on FDO waves. When the oscillation period of the medium increases with the distance from the reactor inlet, it is observed that waves propagate downstream with a decreasing width and velocity. The behavior of both the waves propagating with an oscillatory velocity and those formed in the presence of a frequency gradient can also be understood in terms of phase dynamics.