What can be done with highly correlated variables (>.95 and <-.95)
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.