I am mainly interested in varieties over an algebraic closed field $k$ (or $\mathbb{C}$). The classification of complex surface is established in the last century and known as Enriques–Kodaira classification. In higher dimension, people realized that mild singularities must be taken into account to build a reasonable theory and Mori and others studied Minimal model program, which is the birational classification of algebraic varieties. However, I am more interested in a concrete description of classification, like the Enriques–Kodaira classification (maybe except for general ones). If I understand correctly, Fano threefolds are pretty well-studied in a concrete manner by Mukai and others. Here is my question:

Is there an Enriques–Kodaira-like classification of Fano threefolds? Maybe over $\mathbb{C}$?