  Massive stars are extremely luminous and drive strong winds, blowing a large
part of their matter into the galactic environment before they finally explode
as a supernova. Quantitative knowledge of massive star feedback is required to
understand our Universe as we see it. Traditionally, massive stars have been
studied under the assumption that their winds are homogeneous and stationary,
largely relying on the Sobolev approximation. However, observations with the
newest instruments, together with progress in model calculations, ultimately
dictate a cardinal change of this paradigm: stellar winds are highly
inhomogeneous. Hence, we are now advancing to a new stage in our understanding
of stellar winds. Using the foundations laid by V.V. Sobolev and his school, we
now update and further develop the stellar spectral analysis techniques. New
sophisticated 3-D models of radiation transfer in inhomogeneous expanding media
elucidate the physics of stellar winds and improve classical empiric mass-loss
rate diagnostics. Applications of these new techniques to multiwavelength
observations of massive stars yield consistent and robust stellar wind
parameters.
