The task of time-to-event prediction differs from traditional regression and classification problems, which aim to predict a continuous or discrete variable. The main reason traditional regression and machine learning methods are inappropriate for this task is the presence of censored data. The first part of the thesis presents the basic concepts of survival analysis and provides an overview of traditional methods, as well as adapted machine learning models. In the second part of the thesis, various survival analysis methods were applied to two publicly available datasets. In the German Breast Cancer Study, the aim is to predict the time to breast cancer recurrence, and in the Bank Customer Churn dataset, the time to bank client churn. Among traditional statistical models, the Cox proportional hazards regression model was developed. Among ensemble models, the following were used: Random Survival Forest, Extra Survival Trees, and two models based on Gradient Boosting. Additionally, models based on Support Vector Machines were also tested. For the smaller dataset describing breast cancer recurrence, the best models were the statistically developed Cox proportional hazards model and the Extra Survival Trees. For the larger dataset describing bank churn, the best model was the Random Survival Forest. Generally, it could be observed that ensemble models achieved better results on the larger dataset. Prior to comparing time-to-event prediction methods, an exploratory data analysis was conducted to provide insight into the features that increase or decrease the hazard.