By evolving science, knowledge, and technology, new and precise methods for measuring, collecting, and recording information have been innovated, which have resulted in the appearance and development of high-dimensional data. The high-dimensional data set, i.e., a data set in which the number of explanatory variables is much larger than the number of observations, cannot be easily analyzed by traditional and classical methods, the same as the ordinary least-squares method, and its interpretability will be very complex. Although in classical regression analysis, the ordinary least-squares estimation is the best estimation method if the essential assumptions are met, it is not applicable for high-dimensional data, and in this condition, we need to apply the modern methods. In this research, it is first mentioned the drawbacks of classical methods in the analysis of high-dimensional data and then, it is proceeded to introduce and explain the modern and common approaches of the regression analysis for high-dimensional data same as principal component analysis and penalized methods. Finally, a simulation study and real-world data analysis are performed to apply and compare the mentioned methods in high-dimensional data.