Endogenity or non-orthogonality occurs when the expected value of the error term, conditional on the model's right hand side variables, is not zero. Under this misspecification, the model's estimators are inconsistent. This problem is virtually unavoidable in discrete choice models of, for example, residential choice. The principal technique to treat for the endogeneity problem in a discrete choice model is the control-function method. It consists of the construction of a function that accounts for the endogenous part of the error term which is then included as an additional variable in the model. Alternatively, the latent-variable method can also be viewed as a procedure to address the endogeneity problem in discrete choice models. In this case, the omitted quality attribute which is causing the endogeneity can be considered as a latent-variable and modeled, in a structural equation, as a function of observed variables and may be enhanced through indicators. The main objectives of this paper correspond to the analysis of the similarities and differences among control-function and latent-variable techniques and the exploration of ways by means of which both methods would enhance each other in addressing endogeneity in discrete choice models. This objective is achieved by analyzing the mathematical and statistical properties of both methods and by testing their performance in terms of the correction of the endogeniety problem in a Monte Carlo database. The paper concludes with the analysis of potential future lines of research in this area.