Radiative corrections to the Zemach contribution of the hydrogen hyper
fine splitting are calculated. Their contributions amount to -0.63(3)
ppm to the HFS. The radiative-recoil corrections are estimated to be 0
.09(3) ppm and the heavy particle vacuum polarization shifts the HFS b
y 0.10(2) ppm. The status of the nuclear-dependent contributions is co
nsidered. From the comparison of theory and experiment a proton polari
zability contribution of 3.5(9) ppm is found. The large shift from an
earlier result (0.48(56) ppm) is due to using a more recent proton rad
ius for the Zemach term calculation. The nuclear structure-dependent c
orrections to the difference nu(HFS)(1s) - n(3) nu(HFS)(ns) are also o
btained.