Generally made from bio-plastics and other biodegradable materials, these types of cups offer some environmental benefits, assuming that they are disposed of appropriately: they must be collected separately and composted.
If they end up in landfill they will likely end up degrading anaerobically and releasing methane, just like everything else. They should also not be put in with e.g. plastic or paper recycling, as they will cause contamination.
Although the terms 'compostable' and 'biodegradable' are often used interchangeably, they do not carry the same meaning.
Biodegradation is a natural process where materials are broken down by microorganisms. However, this can take a long time and the by-products will not necessarily be harmless to the environment. Petroleum-based plastics such as polyethylene (PE) can be made 'biodegradable' with the use of additives.
Compostable items, on the other hand, must meet certain specifications around how they biodegrade and what they biodegrade into. They also do not contain petroleum-based materials.
Compostable cups are commonly paper cups with a PLA lining (poly-lactic acid, extracted from renewable resources like corn starch).