Accurate models of H2O and CO2 solubility in silicate melts are vital for understanding volcanic plumbing systems. These models are used to estimate the depths of magma storage regions from melt inclusion volatile contents, investigate the role of volatile exsolution as a driver of volcanic eruptions, and track the degassing path followed by a magma ascending to the surface. However, despite the large increase in the number of experimental constraints over the last two decades, many recent studies still utilize an earlier generation of models which were calibrated on experimental datasets with restricted compositional ranges. This may be because many of the available tools for more recent models require large numbers of input parameters to be hand‐typed (e.g., temperature, concentrations of H2O, CO2, and 8–14 oxides), making them difficult to implement on large datasets. Here, we use a new open‐source Python3 tool, VESIcal, to critically evaluate the behaviors and sensitivities of different solubility models for a range of melt compositions. Using literature datasets of andesitic‐dacitic experimental products and melt inclusions as case studies, we illustrate the importance of evaluating the calibration dataset of each model. Finally, we highlight the limitations of particular data presentation methods, such as isobar diagrams, and provide suggestions for alternatives, and best practices regarding the presentation and archiving of data. This review will aid the selection of the most applicable solubility model for different melt compositions, and identifies areas where additional experimental constraints on volatile solubility are required. Plain Language Summary: Being able to accurately model the solubility of H2O and CO2 in magmas is very important for understanding a wide variety of volcanic processes, such as the depths at which magma is stored in the crust, the driving force behind volcanic eruptions, and the release of volatile elements into the atmosphere. However, there has been no easy way for volcanologists to perform calculations on large datasets, or to compare different models. This review uses a new, open‐source tool called VESIcal written in the popular programming language Python3. This allows us to compare different models for a wide variety of melt compositions, temperatures, and pressures, helping researchers to identify the most suitable model for their study. We also suggest areas where further experimental constraints are required. Finally, we highlight the limitations of particular data presentation methods, such as isobar diagrams, provide suggestions for alternative plots, and best practices regarding the presentation and archiving of data. Key Points: The Python3 tool VESIcal allows extensive comparisons to be drawn between different H2O‐CO2 solubility modelsSolubility models are not interchangeable—for a single magma composition, different models can predict a wide range of solubility relationshipsThe P‐T‐X calibration range of each solubility model must be critically evaluated before application to a specific volcanic system [ABSTRACT FROM AUTHOR]