For a given simple graph G with n vertices, the maximum nullity (respectively, positive semidefinite maximum nullity) of G, denoted by M(G) (respectively, M+(G)) is de ned to be the maximum nullity of all the real symmetric (respectively, positive semide nite) n  n matrices whose (i; j) entries (for i 6= j) are nonzero if and only if the vertices vi and vj are adjacent in G. The problem of determining and/or approximating M(G) (M+(G)) are important deep problems which have attracted considerable attentions in the recent years. In this talk we will describe some of our results concerning the bounds of these parameters. In particular, we will introduce the graph theoretical zero-forcing parameters and discuss how they can bound maximum nullity parameters. As well, we will provide some of our results towards proving the well-known Delta Conjectures of graphs, which state that M(G) (M+(G)) are bounded bellow by the minimum degree of the vertices of the graph.