If you're a Twitter addict (who isn't?) and you have $2.99 to spare, you have to download Tweetbot. Like, NOW.
I'm usually hesitant to download paid apps (like everyone else, yes?), especially when there's a free equivalent out there that does pretty much the same thing, but I am willing to shell out a couple of bucks for really well-designed software.
Now the native Twitter app isn't all that bad, to be honest. It's just not aligned with my usage. For instance, some people I communicate with via Twitter direct messages (because they don't have WhatsApp or iMessage or we just happened to start the conversation there). So I do access my DM inbox frequently. With the Twitter app, I have to go to my profile ("Me") page to access my direct message. With Tweetbot, it's right there in the navigation bar.
I am also quite attached to my lists. Because there are people I follow who tend to flood my timeline (read:celebrities), so much so that the more relevant tweets from people I actually know get buried in the avalanche. So there are times when I prefer to check my lists instead of my timeline. To do this in the native app, I have to go to my profile -> lists -> select lists. In Tweetbot, I can change my Timeline to any one of my lists.
Last but not least: Instagram. With the plethora of people cross-posting their Instagram photos on Twitter you would think the native app would support displaying them instead of just dumbly showing a link. Hmmf.
There are a ton of other things it does better that I won't discuss here, because they don't justify the jump from free to paid app as well as the ones I discussed above (for me, at least). But at any rate, if you use Twitter the same way I do, then you need this. I promise.