Both covariance matrix and variogram matrix functions are used to describe the dependence structure of an multivariate random field with second-order increments. Which are often used to model complex spatial data observed in various disciplines, such as environmental science, climatology and ecology. We will explore how a conditionally negative definite (matrix) function (CNDF) can serve as an important tool in constructing multivariate covariance or variogram matrix functions. The natural connection of CNDF with both variance and covariance- based variogram matrix function is characterized. Several classes of flexible multivariate spatial and spatio-temporal covariance models are derived using the CNDF techniques and mixture methods. Some applications of these models are illustrated using simulation studies.