In sample surveys, the sample units are typically chosen using a complex design. This may lead to a selection effect and, if uncorrected in the analysis, may lead to biased inferences. To mitigate the effect on inferences of deviations from a simple random sample a common technique is to use survey weights in the analysis. This article reviews approaches to address possible inefficiency in estimation resulting from such weighting. To improve inferences we emphasize modifications of the basic design-based weight, that is, the inverse of a unit's inclusion probability. These techniques include weight trimming, weight modelling and incorporating weights via models for survey variables. We start with an introduction to survey weighting, including methods derived from both the design and model-based perspectives. Then we present the rationale and a taxonomy of methods for modifying the weights. We next describe an extensive numerical study to compare these methods. Using as the criteria relative bias, relative mean square error, confidence or credible interval width and coverage probability, we compare the alternative methods and summarize our findings. To supplement this numerical study we use Texas school data to compare the distributions of the weights for several methods. We also make general recommendations, describe limitations of our numerical study and make suggestions for further investigation.