Abstract: It is a fundamental question to ask the distribution of integral solutions to Diophantine equations, which leads to the study of the distribution of integral points on algebraic varieties. In this talk, I will give a brief introduction of the problem formulated under height machinery. We will then discuss two essential tools in Diophantine approximation: the celebrated Subspace Theorem and the filtration method, with various improved versions. Recent results on the approximations and degeneracy of integral points will be outlined as well. In the end, I will introduce the most recent result of keeping good approximations while dropping the restriction of being general position. Joint work with Huang and Levin.