This paper reviews and discusses various bivariate line-fitting methods commonly used in allometry, a field that studies the relationship between size and biological consequences. The authors emphasize the distinction between equation error and measurement error, which has not been widely recognized in the literature. They describe linear regression, major axis (MA), and standardised major axis (SMA) methods, and their applications in allometry. The paper also covers methods for accounting for measurement error in line-fitting, which is crucial when both types of errors are present. Additionally, it provides guidelines for choosing the appropriate method based on the nature of the errors and the research questions. The authors present a geometric interpretation of these methods and discuss their implications for inference, including testing for slopes, elevations, and shifts along the axis. They also introduce novel contributions, such as a method for comparing multiple lines and new methods for inference when no guidance is available. Simulations are conducted to evaluate the performance of these methods, and recommendations are made for future research.This paper reviews and discusses various bivariate line-fitting methods commonly used in allometry, a field that studies the relationship between size and biological consequences. The authors emphasize the distinction between equation error and measurement error, which has not been widely recognized in the literature. They describe linear regression, major axis (MA), and standardised major axis (SMA) methods, and their applications in allometry. The paper also covers methods for accounting for measurement error in line-fitting, which is crucial when both types of errors are present. Additionally, it provides guidelines for choosing the appropriate method based on the nature of the errors and the research questions. The authors present a geometric interpretation of these methods and discuss their implications for inference, including testing for slopes, elevations, and shifts along the axis. They also introduce novel contributions, such as a method for comparing multiple lines and new methods for inference when no guidance is available. Simulations are conducted to evaluate the performance of these methods, and recommendations are made for future research.