Let G be a finite group and F(G) denote the Fitting subgroup of G. Gluck has conjectured that |G : F(G)| should be bounded above by a polynomial in b(G), the largest character degree of G. The bound |G : F(G)| <= b(G)^2 is known to be true for many classes of solvable groups, and the bound |G : F(G)| < b(G)^3 is conjectured to be true for all finite groups. We extend some recent work on Gluck's conjecture for solvable groups, and give a very easy proof, based on the work of Guralnick and Robinson on commuting probabilities, that |G : F(G)| < b(G)^4 for all finite groups. Additionally, we will discuss some recent developments in analyzing the character degree ratio of G, which is defined to be the ratio of the largest character degree with the smallest (nonlinear) character degree of G. This is joint work with H. Nguyen, A. Maroti, and Z. Halasi.