In this section, starting from the definition of the “random error term” that distinguishes econometric models from mathematical models, the focus will be on the assumptions related to the random error term, which make it possible to determine the appropriateness of econometric models. In line with this aim, first and foremost, the most critical assumption, “The conditional expected value of each error term is zero,” will be discussed in detail. The discussion will highlight what this assumption tells researchers, the problems that may arise in practice if it is not satisfied, and potential solutions to those problems. Readers will be directed to reliable sources for theoretical information that can be found in many references, while this book chapter will primarily present subtle but important points, often overlooked between the lines, in a clear and simple manner. Thus, unnecessary repetitions will be avoided, the originality of the chapter will be emphasized, and readers will be able to gain the maximum benefit from it. Possible paths will be evaluated depending on whether the data are cross-sectional or time series. Following the assessment of the critical assumption, other stochastic assumptions will be examined. These include the assumption of constant variance of error terms, the absence of autocorrelation among error terms, the absence of a relationship between independent variables and the error term, and the normal distribution of error terms. The consequences of violations of these assumptions and the corresponding solution proposals will be evaluated together. Where necessary, small application examples, supported by publicly available data and implemented through EViews, Gretl, and R software, will be presented to improve comprehension of theoretical explanations, make theoretical background more visible, and strengthen intuition. Furthermore, throughout the chapter, theoretical discussions will proceed from traditional econometric approaches toward more contemporary ones, without going beyond the scope of the chapter. In this way, the content and title of the subsection will be directly connected to the overall title of the book.