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This paper presents new deep and wide narrow-band surveys undertaken withUKIRT, Subaru and the VLT; a combined effort to select large, robust samples ofH-alpha (Ha) emitters at z=0.40, 0.84, 1.47 and 2.23 (corresponding tolook-back times of 4.2, 7.0, 9.2 and 10.6 Gyrs) in a uniform manner over ~2deg^2 in the COSMOS and UDS fields. The deep Ha surveys reach ~3M_sun/yr out toz=2.2 for the first time, while the wide area and the coverage over twoindependent fields allow to greatly overcome cosmic variance. A total of 1742,637, 515 and 807 Ha emitters are homogeneously selected at z=0.40, 0.84, 1.47and 2.23, respectively, and used to determine the Ha luminosity function andits evolution. The faint-end slope is found to be -1.60+-0.08 over z=0-2.23,showing no evolution. The characteristic luminosity of SF galaxies, L*, evolvessignificantly as log[L*(z)]=0.45z+log[L*(z=0)]. This is the first time Ha hasbeen used to trace SF activity with a single homogeneous survey at z=0.4-2.23.Overall, the evolution seen in Ha is in good agreement with the evolution seenusing inhomogeneous compilations of other tracers of star formation, such asFIR and UV, jointly pointing towards the bulk of the evolution in the last 11Gyrs being driven by a strong luminosity increase from z~0 to z~2.2. Ouruniform analysis reveals an Ha star formation history of the Universe which canbe simply parameterised by log(SFRD)=-2.1/(1+z) for z<2.23. Both the shape andnormalisation of the Ha star formation history are consistent with themeasurements of the stellar mass density growth, confirming that our Haanalysis traces the bulk of the formation of stars in the Universe up to z~2.2.Star formation activity since z~2.2 is responsible for ~95% of the totalstellar mass density observed locally today (with half being assembled betweenz=1.2-2.2, and the rest since z<1.2).

A large H{\alpha} survey at z=2.23, 1.47, 0.84 & 0.40: the 11 Gyr evolution of star-forming galaxies from HiZELS