Finite population inference is a central goal in survey sampling. Probability sampling is the main statistical approach to finite population inference. Challenges arise due to high cost and increasing non-response rates. Data integration provides a timely solution by leveraging multiple data sources to provide more robust and efficient inference than using any single data source alone. The technique for data integration varies depending on types of samples and available information to be combined. This article provides a systematic review of data integration techniques for combining probability samples, probability and non-probability samples, and probability and big data samples. We discuss a wide range of integration methods such as generalized least squares, calibration weighting, inverse probability weighting, mass imputation and doubly robust methods. Finally, we highlight important questions for future research.