Working with Data which is not Normal/Gaussian
There are models that do not make assumption that the underlying data distribution is a normal distribution. 

For example, support vector machine just cares about the boundaries of the separating hyperplane and do not assume the exact shape of the distributions. Decision tree models also do not make such assumption.

Gaussian distribution is popular and it has been analyzed frequently for its simplicity but there are other models as well. 

If you know the distributions that you believed your data can follow, you can also build your own model, for example by maximizing the likelihood or posterior distributrion.

If you are able to convert your data to normal distribution and use a model that you are familiar with, you can try it and see how does it perform.