Muon spin relaxation/rotation (µSR) is a very useful technique for probing the superconducting gap structure, pairing symmetry and time reversal symmetry breaking, enabling an understanding of the mechanisms behind the unconventional superconductivity of cuprates and Fe-based hightemperature superconductors, which remain a puzzle. Very recently double layered Fe-based superconductors having quasi-2D crystal structures and Cr-based superconductors with a quasi-1D structure have drawn considerable attention. Here we present a brief review of the characteristics of a few selected Fe-and Cr-based superconducting materials and highlight some of the major unsolved problems, with an emphasis on the superconducting pairing symmetries of these materials. We focus on µSR studies of the newly discovered superconductors ACa2Fe4As4F2 (A = K, Rb, and Cs), ThFeAsN, and A2Cr3As3 (A = K, Cs), which were used to determine the superconducting gap structures, the presence of spin fluctuations, and to search for time reversal symmetry breaking in the superconducting states. We also briefly discuss the results of µSR investigations of the superconductivity in hole and electron doped BaFe2As2.