Densely time sampled multi-frequency flux measurements of the extreme BL Lac object S5 0716+714 over the past three years allow us to study its broad-band variability, and the detailed underlying physics, with emphasis on the location and size of the emitting regions and the evolution with time. We study the characteristics of some prominent mm-/gamma-ray flares in the context of the shock-in-jet model and investigate the location of the high energy emission region. The rapid rise and decay of the radio flares is in agreement with the formation of a shock and its evolution, if a geometrical variation is included in addition to intrinsic variations of the source. We find evidence for a correlation between flux variations at gamma-ray and radio frequencies. A two month time-delay between gamma-ray and radio flares indicates a non-cospatial origin of gamma-rays and radio flux variations in S5 0716+714.