A number of characterizations of the class of strongly regularDinner matrix-valued functions and descriptions of the corresponding reproducing kernel Hilbert spaces and formulas for the reproducing kernels of these spaces are reviewed. Applications to bitangential interpolation problems, bi-tangential inverse problems for canonical integral and differential systems, J-unitary nodes and Livsic-Brodskii J-nodes are surveyed. Most of the furnished information is adapted from the papers [ArD1]—[ArD11]. However, in the last two sections, some new results are presented.