We establish certain results for several filtrations of smooth and topological knot concordance groups. First, as regards n-solvable filtration of topological knot concordance group, C, defined by K. Orr, P. Teichner and first author: 0 ⊂... ⊂ F (n,.5) ⊂ F (n) ⊂... ⊂ F (1.5) ⊂ F (1.0) ⊂ F (0.5) ⊂ F (0) ⊂ C, we refine recent nontriviality results of Cochran and Teichner by including information on Alexander modules. These results also extend those of C. Livingston and second author. We exhibit similar structure in closely related symmetric Grope filtration ofC. We also show that Grope filtration of smooth concordance group is nontrivial using examples that cannot be distinguished by Ozsvath-Szabo τ-invariant nor by J. Rasmussen's s-invariant. Our broader contribution is to establish, in the relative case, key homological results whose analogues Cochran-Orr-Teichner established in the absolute case. We say two knots K 0 and K 1 are concordant modulo n-solvability if K o #(-K 1 ) ∈F (n) . Our main result is that, for any knot K whose classical Alexander polynomial has degree greater than 2, and for any positive integer n, there exist infinitely many knots K i that are concordant to K modulo n-solvability, but are all distinct modulo n.5-solvability. Moreover, K i and K share same classical Seifert matrix and Alexander module as well as sharing same higher-order Alexander modules and Seifert presentations up to order n - 1.