Although it is never the first thing that comes to mind when you think about a movie, aspect ratios play a big part in what comes to stylistic marks. It limits everything you can or can’t show, literally.
And this was actually a big problem not so long ago. For example, with the growth of television and the changes of the mainstream television ratios over the years, directors had to choose for which media they were producing and edit their films based on that. Bringing some problems to more-wider-ratios-fans directors and limiting the options of image composition.
But besides this kind of technical issues and the strong connection to a certain time period, it can also imply heavy stylistic and narrative choices of the filmmakers. In this video from Fandor, Jacob T. Swinney explores the many ways some of the most highly regarded filmmakers have used different aspect ratios as a storytelling device.