Optimal transport describes the process of finding the most efficient way to move mass between two distributions. Wasserstein distance measures the minimal transportation cost achieved by that optimal plan. However, in higher dimensions, computing the Wasserstein distance becomes computationally expensive. The sliced Wasserstein distance offers an effective and efficient way to alleviate this burden. In this talk, I will talk about the quantitative estimates between the sliced 1-Wasserstein distance and the 1-Wasserstein distance. I will then discuss our construction of a concrete example that demonstrates the exponents in the estimate are sharp. This is joint work with Guillaume Carlier, Alessio Figalli, Quentin Merigot.