This review discusses bivariate line-fitting methods for allometry, focusing on the appropriate methods for estimating relationships between two variables. It highlights the importance of distinguishing between measurement error (error in observed values) and equation error (error in the relationship between variables). These errors have different implications for choosing line-fitting methods. Linear regression, major axis (MA), and standardised major axis (SMA) are alternative methods that can be appropriate when there is no measurement error. When measurement error is present, it needs to be estimated and used to adjust variance terms in line-fitting formulae. The review also covers line-fitting methods for phylogenetic analyses. The paper discusses methods of inference for line-fitting techniques, including testing if the slope or elevation equals a given value, constructing confidence intervals for the slope or elevation, comparing several slopes or elevations, and testing for shift along the axis among several groups. It also addresses the robustness of inferential procedures to assumptions and provides software recommendations. The review identifies key points, including the distinction between measurement and equation error, the use of different line-fitting methods depending on the presence of error, and the importance of considering the context of the data. It also discusses the use of simulation to assess the performance of inference methods and provides guidelines for estimating measurement error variance. The paper concludes that the choice of line-fitting method depends on the nature of the data and the research question, and that methods such as MA and SMA are appropriate when both measurement and equation errors are present. It also highlights the importance of considering the implications of measurement error in allometric studies and provides guidance on how to account for it in line-fitting and inference procedures.This review discusses bivariate line-fitting methods for allometry, focusing on the appropriate methods for estimating relationships between two variables. It highlights the importance of distinguishing between measurement error (error in observed values) and equation error (error in the relationship between variables). These errors have different implications for choosing line-fitting methods. Linear regression, major axis (MA), and standardised major axis (SMA) are alternative methods that can be appropriate when there is no measurement error. When measurement error is present, it needs to be estimated and used to adjust variance terms in line-fitting formulae. The review also covers line-fitting methods for phylogenetic analyses. The paper discusses methods of inference for line-fitting techniques, including testing if the slope or elevation equals a given value, constructing confidence intervals for the slope or elevation, comparing several slopes or elevations, and testing for shift along the axis among several groups. It also addresses the robustness of inferential procedures to assumptions and provides software recommendations. The review identifies key points, including the distinction between measurement and equation error, the use of different line-fitting methods depending on the presence of error, and the importance of considering the context of the data. It also discusses the use of simulation to assess the performance of inference methods and provides guidelines for estimating measurement error variance. The paper concludes that the choice of line-fitting method depends on the nature of the data and the research question, and that methods such as MA and SMA are appropriate when both measurement and equation errors are present. It also highlights the importance of considering the implications of measurement error in allometric studies and provides guidance on how to account for it in line-fitting and inference procedures.