Estimation of mixing coeficients in a mixture distribution has a variety of applications in machine learning. For example, under class prior shift, estimation of class priors from labeled training data and unlabeled test data plays an essential role in adaptation; for enabling positive-unlabeled classification, class prior estimation only from positive and unlabeled data is a key challenge; and to cancel the bias caused by label noise, estimation of the noise transition is a central task. In this talk, I will give an overview of our advances in mixture proportion estimation and their use in various machine learning tasks.