This talk provides an overview of my work during my Ph.D. studies. The classical Murnaghan-Nakayama rule is a combinatorial formula that computes the irreducible characters of the symmetric group iteratively. Since then, many generalizations of this formula have been established, with one of the most notable being the q-version of the Murnaghan-Nakayama rule for the Hecke algebra in type A, introduced by Ram in 1991. In this talk, I will present a new method, using vertex operators, to revisit the q-Murnaghan-Nakayama rule. This method also extends to the Murnaghan-Nakayama rule for the Hecke-Clifford algebra, which was previously unknown for a long time. More broadly, a multi-parameter Murnaghan-Nakayama rule for the Macdonald polynomials is derived, unifying these two rules. Finally, I will discuss our most recent result: a Murnaghan-Nakayama rule for the Ariki-Koike algebra utilizing λ-ring theory. These are joint works with my doctoral supervisor, Prof. Naihuan Jing.