The sparse (or toric) resultant generalizes the classical resultant and exploits the sparseness of the input polynomials defined by their Newton polytopes. This talk focuses on sparse resultant matrices of Sylvester-type, which reduce system-solving to an eigenproblem and also lead to a Macaulay-type formula. We also discuss perturbations for handling degenerate inputs and the quasi-Toeplitz structure of the matrices.