Twitter has dropped support for RSS Feeds but there does exist a solution, slightly complicated though, that you may use to generate feeds for your various Twitter streams including Twitter search results, user timelines and even Twitter lists.
Without RSS feeds, it is difficult to use your Twitter data elsewhere. For instance, you can no longer create recipes in IFTTT that get triggered when you post a new tweet. You cannot import your Twitter timeline automatically into your blog. You cannot track Twitter search results for certain keywords in your RSS reader.