Non-randomised studies (NRS) typically assume that there are no differences in unobserved baseline characteristics between the treatment groups under comparison. Traditionally regression models have been deployed to estimate treatment effects adjusting for observed confounders but can lead to biased estimates if the model is missspecified, by making incorrect functional form assumptions. A multitude of alternative methods have been developed which can reduce the risk of bias due to model misspecification. Investigators can now choose between many forms of matching, weighting, doubly robust, and machine learning methods. We review key concepts related to functional form assumptions and how those can contribute to bias from model misspecification. We then categorize the three frameworks for modeling treatment effects and the wide variety of estimation methods that can be applied to each framework. We consider why machine learning methods have been widely proposed for estimation and review the strengths and weaknesses of these approaches. We apply a range of these methods in re-analyzing a landmark case study. In the application, we examine how several widely used methods may be subject to bias from model misspecification. We conclude with a set of recommendations for practice.