Kotlin is what Java would have been if it had been designed today. It follows the same philosophy: emphasis on readability, familiarity and maintainability, with PL research and new paradigms being non-goals. It does not introduce new concepts that will revolutionize your development, opting instead to adopt a few well-proven features (null safety, data classes). It is very easy to learn, feels modern and fun. Kotlin offers only a minimal runtime library, instead focusing on making the Java libraries more fun to use. Compilation is fast, and performance is about identical to that of Java.

While other languages promise a huge productivity boost (though few deliver) at a high switching cost, using Kotlin is practically free. It interoperates with Java so smoothly that you can gradually transition by freely mixing Java and Kotlin files in the same package. Calling and passing objects from Kotlin to Java and vice-versa is nearly seamless.

IDE support is world-class, and Kotlin is the only language other than Java (AFAIK) that lets you use annotation processors, so you can make use of, say, Dagger's compile time verification of dependencies.

My favorite feature is smart casting. Inline functions are a poor-man's macros: powerful enough for many things, yet not too clever to be potentially confusing.

The only concerns are with adoption rates, and whether the evolutionary progress justifies a new language. I think that the extremely low switching costs make it at the very least worth a try. Why not start with a mixed Java/Kotlin project?