The Twitter Streaming API gives you access to multiple types of streams (public, user, site), with the difference that the streaming API collects data in real-time (as opposed to the search API, which retrieves past tweets). I setup a server on digital ocean to collect the tweets about ehtereum for a longer time.
I will use this data for algorithmic trading of cryptocurrency based on twitter sentiment analysis because past research from Stanford has shown that real-time Twitter data can be used to predict market movement of securities and other financial instruments. The goal is to prove whether Twitter data relating to cryptocurrencies can be utilized to develop advantageous crypto coin trading strategies.
NOTE: An interesting dataset can be found here: https://github.com/mluders/tweetwise