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Logistic regression is a statistical model that helps to deal with binary classification problems. In the classic setting where the number of regressors p is fixed and the sample size n becomes increasingly large, the maximum likelihood estimator (MLE) holds good properties and the likelihood ratio test statistic is known to follow a chi-squared distribution. Modern data often have high-dimensional structures where n and p both grow, and p is not negligible compared with n. Recently, Sur and Candès (2019) and Zhao et al. (2020) investigated the MLE and the distribution of the likelihood ratio test statistic for logistic models in such high-dimensional setting. The studies proved three main results: for a high-dimensional logistic model, 1) the classic MLE is no longer unbiased, 2) the variability of the MLE is larger than what classically estimated, and 3) the likelihood ratio test statistic follows a rescaled chi-squared distribution with a scaling factor for adjustment. In this thesis, we conducted simulations in different well-motivated scenarios with synthetic data to either verify the conclusions for high-dimensional logistic models or explore other phenomena of interests, which includes but not limited to 1) verifying of the conclusions about the MLE and distribution of likelihood ratio test statistic in high dimensions with comparisons of classic and adjusted results, 2) exploring whether the same scaling factor also works for Wald test and Score test in high dimensions, and 3) investigating the performance of the scaling factor when the model is misspecified. Lastly, we applied the high-dimensional knowledge to real-world data to fit logistic models and conduct hypothesis tests to illustrate the practical behaviour and applicability.