As mentioned before, Java interoperability was one of the main goals during the development of Kotlin and it is implemented seamlessly. You can call from Kotlin existing libraries compiled with Java; you can also extend a class written in Java or implement an interface written in Java and use all its types from the Java Standard Library.
But the best part is that you can have Kotlin side-by-side with the existing Java code. There's nothing preventing you from writing half of your project in Java and the other half in Kotlin.
IDEs (IntelliJ or Eclipse with a Kotlin plugin) support navigating in both Kotlin and Java files in the same project. Also, debugging and stepping through code from a project with both languages is not a problem at all. Refactoring Kotlin or Java code will also correctly update the references in another language as well.
This interoperability is also visible in the Kotlin Standard Library. Standard Library relies heavily on Java Standard Library and extends a lot of types from it. For example, Kotlin doesn't have it's own collections classes, it uses ones from Java. Java library has been battle tested and so it wouldn't make sense to reinvent the wheel.
Java-Kotlin interoperability also works in another direction. You can call functions written in Kotlin from Java, extend types and implement interfaces declared in Kotlin.
