This dissertation concerns the use of logistic regression when certain standard model assumptions are violated. Chapters I and II study the problem of estimating regression parameters when covariates are subject to measurement error. The latter chapters study robust methods applicable to logistic regression. To facilitate study of the errors-in-variables problem a small measurement error asymptotic theory is developed. This allows comparison of certain estimators which have appeared in the literature and also suggests new estimators which are shown to have better asymptotic properties. A small Monte-Carlo study confirms the superiority of the new estimators in certain settings. In the course of studying the asymptotic behavior of the various estimators interesting use is made of some random convex analysis. To deal with the problem of messy data, i.e. outliers and extreme covariables, several bounded influence estimators are proposed. The optimality properties of these estimators are studied in Chapter III. Asymptotic theory for the robust procedures is given in Chapter IV. Finally, Chapter V concludes the thesis with an application of these methods to two sets of data.