A Laplacian matrix, $L=(\l_{ij})\in\R^{n\times n} $, has nonpositiveoff-diagonal entries and zero row sums.As a matrix associated with a weighted directed graph, it generalizes theLaplacian matrix of an ordinarygraph. A standardized Laplacian matrix is a Laplacian matrix with $-{1\overn}\le\l_{ij}\le0$ at $j\ne i.$ Westudy the spectra of Laplacian matrices and relations between Laplacianmatrices and stochastic matrices. Weprove that the standardized Laplacian matrices $\LT$ are semiconvergent. Themultiplicities of $0$ and $1$ asthe eigenvalues of $\LT$ are equal to the in-forest dimension of thecorresponding digraph and one less thanthe in-forest dimension of the complementary digraph, respectively. Welocalize the spectra of thestandardized Laplacian matrices of order $n$ and study the asymptoticproperties of the corresponding domain.One corollary is that the maximum possible imaginary part of an eigenvalueof $\LT$ converges to${1\over\pi}$ as $n\to\infty.$