k-Factorization and Next-to-leading BFKL Kernel

I review recent results by Fadin,Lipatov and collaborators and by our group,leading to the almost complete calculation of the next-to-leading BFKL kernel,of its eigenvalues,and of the resummed gluon anomalous dimension. Qualitative implications for small-x structure functions include consistent running coupling effects and a sizeable decrease of the Pomeron intercept,so as to slow down the small-x rise at low values of Q