Incremental delta-sigma analog-to-digital converters (IADC) are widely used in modern high-fidelity audio, sensors, and 1oT low-power applications. Over the past years, the techniques to implement high-resolution lADCs have been significantly improved, (a) for example, in handling the weighting problems inside the lADCs to overcome thermal noise and DAC mismatch issues. This paper offers a tutorial review on the considerations of weightings in lADCs. The influence of weightings on thermal noise and DAC mismatches is analyzed, and the use of weighting in algorithms is described specifically. The advanced architectures to take advantage of the weightings based on recent academic achievements are presented respectively, with design examples to illustrate the successful practical implementations.