We explore the role of environment in the evolution of galaxies over 0.1 \textless z \textless 0.7 using the final zCOSMOS-bright data set. Using the red fraction of galaxies as a proxy for the quenched population, we find that the fraction of red galaxies increases with the environmental overdensity delta and with the stellar mass M-*, consistent with previous works. As at lower redshift, the red fraction appears to be separable in mass and environment, suggesting the action of two processes: mass epsilon(m)(M-*) and environmental epsilon(rho)(d) quenching. The parameters describing these appear to be essentially the same at z similar to 0.7 as locally. We explore the relation between red fraction, mass and environment also for the central and satellite galaxies separately, paying close attention to the effects of impurities in the central-satellite classification and using carefully constructed samples well matched in stellar mass. There is little evidence for a dependence of the red fraction of centrals on overdensity. Satellites are consistently redder at all overdensities, and the satellite quenching efficiency, epsilon(sat)(delta, M-*), increases with overdensity at 0.1 \textless z \textless 0.4. This is less marked at higher redshift, but both are nevertheless consistent with the equivalent local measurements. At a given stellar mass, the fraction of galaxies that are satellites, f(sat)(delta, M-*), also increases with overdensity. The obtained epsilon(rho) (delta)/f(sat)(delta, M-*) agrees well with epsilon(sat)(delta, M-*), demonstrating that the environmental quenching in the overall population is consistent with being entirely produced by a satellite quenching process at least up to z = 0.7. However, despite the unprecedented size of our high-redshift samples, the associated statistical uncertainties are still significant and our statements should be understood as approximations to physical reality, rather than physically exact formulae.