It is well known that the rational (or Padé) approximants are closely related with the discrete-time Toda equation. The structural connection with orthogonal polynomials provides a link between the theory of integrable systems and various classical results of applied mathematics and numerical analysis. Inspired by recent advances on symmetry and integrability of difference equations I would like to disuss several generalizations of the relation (some of them already known): * the role of Hirota's discrete KP system; * non-commutative versions of the classical results; * approximation as a confluent limit of the interpolation. [1] A. Doliwa, A. Siemaszko, Integrability and geometry of the Wynn recurrence, Numer. Algorithms doi: 10.1007/s11075-022-01344-5 [2] A. Doliwa, A. Siemaszko, Hermite-Padé approximation and integrability, arXiv:2201.06829 [3] A. Doliwa, Non-commutative Hermite-Padé approximation and integrability, Lett. Math. Phys. 112 68 (2022) doi: 10.1007/s11005-022-01560-z [4] A. Doliwa, Non-autonomous multidimensional Toda system and multiple interpolation problem, J. Phys. A: Math. Theor. 55 (2022) 505202 (17 pp.) doi: 10.1088/1751-8121/acad4d