The Central Limit Theorem (CLT) plays an indispensable role in classical statistical inference for finite-dimensional parameters, including calibration of confidence sets and statistical tests. However, the validity of the CLT in high dimensional problems where the dimension (p) of the observations diverges to infinity with the sample size (n) is no longer guaranteed. There is extensive recent work on the problem, following the seminal paper by Chernozhukov, Chetverikov, and Kato (2013; Annals of Statistics), that attempts to establish the CLT (or Gaussian Approximation) in high dimensions under various growth conditions on the dimension p. In this talk, we present some new results on Gaussian Approximation for different classes of sets, providing insights into specific distributional characteristics of the underlying high dimensional random vectors that determine the optimal growth rates.