The Invariance principle is an extension of the Central Limit Theorem on high-order polynomials, which is widely used in various fields of theoretical computer science such as learning theory, de randomization, and non approximation theory. This principle establishes a bridge between continuous mathematics and discrete mathematics, and is also an important theoretical tool for computational complexity. This report will introduce the principle of invariance and its latest applications in computational complexity and quantum computing. If time permits, we will introduce some public issues in the current direction.