Wilf’s conjecture establishes an inequality that relates three fundamental invariants of a numerical semigroup: the minimal number of generators (or the embedding dimension), the Frobenius number, and the number of gaps. Based on a preprint by Srinivasan and S-, the talk will discuss the past, present, and future of this conjecture. We prove that this Wilf inequality is preserved under gluing of numerical semigroups.  If the numerical semigroups minimally generated by \(A = \{ a_1, \ldots, a_p\}\) and \(B = \{ b_1, \ldots, b_q\}\) satisfy the Wilf inequality, then so does their gluing which is minimally generated by \(C =k_1A\sqcup k_2B\). We discuss the extended Wilf's Conjecture in higher dimensions and prove an analogous result.