In practice, often people don't know if graphs will be planar or if they should expect it. However this is great work for specialists. In the graph drawing community, work that focused on planar graphs has been quite elegant but applications are not that widespread.
Heh, found this game:<p><a href="https://www.jasondavies.com/planarity/" rel="nofollow noreferrer">https://www.jasondavies.com/planarity/</a>