Continuations have received considerable attention lately as a possible solution to web application development. Other uses proposed in the past, such as cooperative threading, coroutines or writing iterators, made them an attractive feature of dynamically typed languages. We present issues involved in adding continuations to a statically typed, object-oriented language like Java, and its implementation in the Java Virtual Machine. We propose three different flavors of continuations, and study their interactions with the base language, focusing on Java's concurrency model. We describe our implementation in Ovm, a realtime Java Virtual Machine, and discuss open issues.