Uncontrolled confounding due to unmeasured confounders biases causal inference in health science studies using observational and imperfect experimental designs. The adoption of methods for analysis of bias due to uncontrolled confounding has been slow, despite the increasing availability of such methods. Bias analysis for such uncontrolled confounding is most useful in big data studies and systematic reviews to gauge the extent to which extraneous preexposure variables that affect the exposure and the outcome can explain some or all of the reported exposure-outcome associations. We review methods that can be applied during or after data analysis to adjust for uncontrolled confounding for different outcomes, confounders, and study settings. We discuss relevant bias formulas and how to obtain the required information for applying them. Finally, we develop a new intuitive generalized bias analysis framework for simulating and adjusting for the amount of uncontrolled confounding due to not measuring and adjusting for one or more confounders.