It's configurable, so my tweets auto-delete after 30 days unless 5+ people favorite or re-tweet them. The Ruby script has been running for several years now on my desktop without any issues (I'm using anacron on Ubuntu, because the computer is off at night when cron would normally run)
There are third-party services available but I won't grant them access to my account and I prefer to do it myself.
Last time I did a Twitter pruning session to remove unwanted drivel, I did it manually and it took me a couple of hours. Thank God I'm only an occasional Twitterer, so I only had a couple of hundred to wade through.
What I'm really waiting for though, to make good on my desire to abandon Twitter completely, is for alternatives like GNUsocial[0] to offer the ability to import your existing Twitter archive. But, as is so often the case with open source projects, they prefer to fuck about with "me too" enhancements like adding 'transgender muslim emoji' support, rather than actually providing incentives for people to migrate easily from Twitter.