We will give a short survey of Alexander Borichev's work on sampling and interpolation in spaces of analytic functions and on related geometric properties of systems of reproducing kernels. In particular, we discuss a surprising construction of Fock-type spaces admitting Riesz bases of normalized reproducing kernels due to A. Borichev and Yu. Lyubarskii as well as several of its consequences. Another group of questions is related to the so-called spectral synthesis problem which was solved in our joint work with Yu. Belov and A. Borichev for the Paley-Wiener, de Branges and Bargmann-Fock spaces. This line of research culminated in the solution (by Borichev and Belov) of the Newman-Shapiro spectral synthesis problem which remained open for more than 50 years.