The team behind Mastodon provide free apps to use for iOS and Android, which you can find on the joinmastodon.org site, but here’s a few apps people like.
These apps work great with social.mastodon.site and all of the fully-managed mastodon servers we run for our customers.

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iOS (iPhone + iPad)

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Android

Mastodon 101 - how to get started

So you want to try out Mastodon? here’s everything you need to know.