One of areas where big data are collected is in environmental and climate studies. The Global Circulation Models or Regional Circulation Models can generate huge amount of data in space and time. Data collected through remote sensing or sensor networks are also huge. All these data are correlated spatially and temporally. One therefore has to deal with the huge covariance matrix in the traditional likelihood-based inferences or Bayesian inferences. When the dimension is very large, inversion of the matrix becomes infeasible numerically and also unstable due to the ill condition of the matrix. The issue becomes more complex when multivariate data are observed which can have different spatial scales. In this talk, I will discuss some recent developments in the theory and methods for dealing with the big spatial data, and in particular highlight some numerical algorithms that are applicable to large multivariate spatial data that are possibly of different scales.