How do I implement a Java interface in Clojure

With proxy

See the proxy macro. Clojure Docs have some examples. It's also covered on Java Interop page.

(proxy [Doer] []
  (doSomethin [input]
    (str input " went through proxy")))

proxy returns an object implementing Doer. Now, to access it in Java you have to use gen-class to make your Clojure code callable from Java. It's covered in an answer to the "Calling clojure from java" question.

With gen-class

(ns doer-clj
  (:gen-class
    :name DoerClj
    :implements [Doer]
    :methods [[doSomethin [String] String]]))

(defn -doSomethin
  [_ input]
  (str input " went through Clojure"))

Now save it as doer_clj.clj, mkdir classes and compile it by calling in your REPL (require 'doer-clj) (compile 'doer-clj). You should find DoerClj.class ready to be used from Java in classes directory

For a more general take on this question, this diagram can be freaking useful when you are in need for some kind of Java-interop:

https://github.com/cemerick/clojure-type-selection-flowchart

reify is strongly preferred for implementing interfaces - proxy is heavy-duty, old, and slow, so should be avoided when possible. An implementation would look like:

(reify Doer
  (doSomethin [this input]
    (...whatever...)))

As of Clojure 1.6, the preferred approach would be as follows. Assuming you have, on your classpath, the Clojure 1.6 jar and the following clojure file (or its compiled equivalent):

(ns my.clojure.namespace
  (:import [my.java.package Doer]))

(defn reify-doer
  "Some docstring about what this specific implementation of Doer
  does differently than the other ones. For example, this one does
  not actually do anything but print the given string to stdout."
  []
  (reify
    Doer
    (doSomethin [this in] (println in))))

then, from Java, you could access it as follows:

package my.other.java.package.or.maybe.the.same.one;

import my.java.package.Doer;
import clojure.lang.IFn;
import clojure.java.api.Clojure;

public class ClojureDoerUser {
    // First, we need to instruct the JVM to compile/load our
    // Clojure namespace. This should, obviously, only be done once.
    static {
        IFn require = Clojure.var("clojure.core", "require");
        require.invoke(Clojure.read("my.clojure.namespace"));
        // Clojure.var() does a somewhat expensive lookup; if we had more than
        // one Clojure namespace to load, so as a general rule its result should
        // always be saved into a variable.
        // The call to Clojure.read is necessary because require expects a Clojure
        // Symbol, for which there is no more direct official Clojure API.
    }

    // We can now lookup the function we want from our Clojure namespace.
    private static IFn doerFactory = Clojure.var("my.clojure.namespace", "reify-doer");

    // Optionally, we can wrap the doerFactory IFn into a Java wrapper,
    // to isolate the rest of the code from our Clojure dependency.
    // And from the need to typecast, as IFn.invoke() returns Object.
    public static Doer createDoer() {
        return (Doer) doerFactory.invoke();
    }
    public static void main(String[] args) {
        Doer doer = (Doer) doerFactory.invoke();
        doer.doSomethin("hello, world");
    }
}