I've been using Google's new Gboard for iOS, and it's quickly become my keyboard of choice on my iPhone. The success rate of third-party keyboards varies widely (Swype proved to be useless to me, and I don't use the Copied keyboard as much as I imagined I would), but Google has combined a bunch of powerful features into what feels like a keyboard that fits modern texting, Tweeting and emailing habits.
The keyboard enables you to search Google directly from your keyboard -- you can look up a quick fact, or copy/paste a search result right there. There's also a dedicated search area for GIFs, so anyone can seem like a GIF master without having to devote a bunch of space in your Photos library to dumb stuff. The Gboard even adds the "swype" technology for when you can only get one hand on your phone.
Perhaps the most underrated feature is how Gboard integrates Emojis. Type a feeling or other form of Emoji search (sad, happy, beer, celebration, "soon"), and Gboard will show Emojis in the "suggested words" area of the keyboard; if you want to look at the full Emoji keyboard, you can do that too, and it's within Gboard rather than being a separate keyboard like Apple's setup. This makes switching faster.
There are a few bugs and improvements to be made. As with any iOS area where a third party invades a historically native space, sometimes Gboard just doesn't load as fast as you'd expect. This is rare but can be annoying if you have to quit an app and restart it to fix the issue. There's also no dark mode, which I'd like to see Google add soon.
At the moment, Gboard is my only iPhone keyboard and unless it starts failing more often, I don't see myself going back to the combo of Apple's English keyboard + Apple's Emoji keyboard.