Companies have had different ways of dealing with and reducing waste, especially in regards to coffee consumption. The most common methods consist simply of using recyclable materials (phasing out disposable plastic entirely, such as with cups and straws). But not even those are necessarily 100% recyclable, since lids tend to be plastic, and plastic liners are used (they serve as a seal so that your paper cup won’t leak).
Other solutions are people bringing their own cups (or Starbuck’s rent cups), of which isn’t the most convenient. The A&W (Canada) restaurant chain came up with a simple solution, to just make it all in one. No straw, no lid, no plastic, completely paper, and has a water-based lining. As a result, the cup is also 100% recyclable and compostable, without any further processing. I hope similar cup designs come into existence all across the globe.