If you are moving onto an old jquery style codebase (via inheriting/changing job) Vue.js can be used as a straight drop in library via a script tag and you can start unsouping that jquery mess.
It also reminds me a lot of a spiritual successor to KnockoutJS (which was/is my favourite JS clientside tool still).
I'm using it with nuxtjs to achieve server side rendering, the benefits of that being faster pageloads on first arrival and faster pageloads for SEO ranking.
React.js is probably the most similar popular framework because of its one-way data binding. Vue's creator (Evan You) wrote a Comparison with Other Frameworks (http://vuejs.org/v2/guide/comparison.html) that's worth reading. Dan Abramov, co-author of Redux, helped keep the comparison with React grounded.
Vue is a reactive JS framework, similar to React or Angular. It's lighter weight, but comes with less built in. It's a very nice framework to work with, easy to get up and running, but powerful enough to build a full featured web app.