1. Upper atmosphere: This layer is composed mostly of hydrogen and helium, and it's where the Great Dark Spot and other storms are found.

2. Lower atmosphere: This layer is thicker and denser than the upper atmosphere, and it contains methane, ammonia, and water ice.

3. Mantle: This layer is composed mostly of water, methane, and ammonia, and it's believed to be extremely hot and dense.

4. Core: This layer is believed to be a solid, rocky core that's about twice the size of Earth.

5. Inner core: This layer is the very center of Neptune, and it's believed to be composed of iron and nickel.

While there are five distinct layers, it's important to note that the boundaries between them are not sharply defined.