What can be done with highly correlated variables (>.95 and <-.95) I hope we can remove the highly correlated variables based on the feature importance may be with PCA etc. 

Is there anything we can do with highly correlated variables/ 

Thanks in advance !
An alternative to the one provided by @Kasra is dimensionality reduction. It's another way of solving your multicollinearity problems, while avoiding deleting variables more or less arbitrarily.

You can use simpler, linear techniques such as PCA, or more complex non-linear techniques such as Autoencoders. t-SNE is a non-linear technique that is typically used for visualization, I do not recommend to use it for a Training set.