We've had a mask mandate in Illinois since May 1. There's no way to tell if or how well they worked in offices and other workplaces, but I believe they help to some extent, even if it's just to lessen the amount of virus being transmitted person to person. One problem I've noted since the beginning of the mandate is that people do not wear the masks correctly.
From what I see, there is very high compliance with mask-wearing in places like stores, where people rarely spend enough time to actually become infected. I suspect the real issue is with non-compliance in workplaces that are not open to the public and in homes. This is probably where the greatest spread is occurring. I wish there was greater emphasis on stressing the danger of indoor gatherings and listing the types of precautions people should be taking if they are gathering indoors. I believe adhering to those precautions would help, but all we hear is "wear a mask," with no additional information or guidance.