We present a comprehensive study of inclusive hadron production in deep inelastic scattering (DIS) at low x. Properties of the hadron spectrum are different in different kinematic regions formed by three relevant momentum scales: photon virtuality Q2, hadron transverse momentum k T and the saturation momentum Q s(x). We investigate each kinematic region and derive the corresponding asymptotic formulas for the cross section at the leading logarithmic order. We also analyze the next-to-leading-order corrections to the Balitskii-Fadin-Kuraev-Lipatov kernel that are responsible for the momentum conservation. In particular, we establish the asymptotic behavior of the forward elastic dipole-nucleus scattering amplitude at high energies deeply in the saturation regime and a modification of the pomeron intercept. We study the nuclear effect on the inclusive cross section using the nuclear modification factor and its logarithmic derivative. We argue that the later is proportional to the difference between the anomalous dimension of the gluon distribution in nucleus and in proton and thus is a direct measure of the coherence effects. To augment our arguments and present quantitative results we performed numerical calculations in the kinematic region that may be accessible by the future DIS experiments.