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The structural identifiability and the observability of a model determine the possibility of inferring its parameters and states by observing its outputs. These properties should be analysed before attempting to calibrate a model. Unfortunately, such \textit{a priori} analysis can be challenging, since it requires symbolic calculations that often have a high computational cost. In recent years a number of software tools have been developed for this task, mostly in the systems biology community but also in other disciplines. These tools have vastly different features and capabilities, and a critical assessment of their performance is still lacking. Here we present a comprehensive study of the computational resources available for analysing structural identifiability. We consider 12 software tools developed in 7 programming languages (Matlab, Maple, Mathematica, Julia, Python, Reduce, and Maxima), and evaluate their performance using a set of 25 case studies created from 21 models. Our results reveal their strengths and weaknesses, provide guidelines for choosing the most appropriate tool for a given problem, and highlight opportunities for future developments.