Abstract: It is a highly celebrated issue in dyadic harmonic analysis the pointwise convergence of the Fejér (or (C,1)) means of functions on the Walsh and Vilenkin groups both in the point of view of one and two dimensional cases. We give a résumé of the very recent developments concerning this matter, propose unsolved problems and throw a glance at the investigation of Vilenkin-like systems too.
Keywords: Vilenkin group, Vilenkin series, Fejer means, a.e. convergence, two-dimensional systems.