For reliable machine learning, overcoming the distribution shift is one of the most important challenges. In this talk, I will first give an overview of the classical importance weighting approach to distribution shift adaptation, which consists of an importance estimation step and an importance-weighted training step. Then, I will present a more recent approach that simultaneously estimates the importance weight and trains a predictor. Finally, I will discuss a more challenging scenario of continuous distribution shifts, where the data distributions change continuously over time.