In this talk we will discuss low and high roads of some results in Matrix Theory. The topics include Schur-Horn theorem on the diagonal elements and eigenvalues and a Hermitian matrix, Thompson's theorems on the diagonal elements and singular values of a complex matrix and a real matrix respectively, Toeplitz-Hausdorff theorem on the convexity and numerical range of a complex matrix, and if time permits, Weyl’s problem and its solution on the spectrum of sum of two Hermitian matrices, etc.