Neural networks solving real-world problems are often required not only to make accurate predictions but also to provide a confidence level in the forecast. The calibration of a model indicates how close the estimated confidence is to the true probability. This paper presents a survey of confidence calibration problems in the context of neural networks and provides an empirical comparison of calibration methods. We analyze problem statement, calibration definitions, and different approaches to evaluation: visualizations and scalar measures that estimate whether the model is well-calibrated. We review modern calibration techniques: based on post-processing or requiring changes in training. Empirical experiments cover various datasets and models, comparing calibration methods according to different criteria.