diff --git a/doc/api/repl.md b/doc/api/repl.md
index 0ebd5ca4e6f465..c26b2a56dc8ad5 100644
--- a/doc/api/repl.md
+++ b/doc/api/repl.md
@@ -709,6 +709,9 @@ npx codemod@latest @nodejs/repl-builtin-modules
 <!-- YAML
 added: v0.1.91
 changes:
+  - version: REPLACEME
+    pr-url: https://github.com/nodejs/node/pull/62188
+    description: The `handleError` parameter has been added.
   - version: v24.1.0
     pr-url: https://github.com/nodejs/node/pull/58003
     description: Added the possibility to add/edit/remove multilines
@@ -787,6 +790,17 @@ changes:
     previews or not. **Default:** `true` with the default eval function and
     `false` in case a custom eval function is used. If `terminal` is falsy, then
     there are no previews and the value of `preview` has no effect.
+  * `handleError` {Function} This function customizes error handling in the REPL.
+    It receives the thrown exception as its first argument and must return one
+    of the following values synchronously:
+    * `'print'` to print the error to the output stream (default behavior).
+    * `'ignore'` to skip all remaining error handling.
+    * `'unhandled'` to treat the exception as fully unhandled. In this case,
+      the error will be passed to process-wide exception handlers, such as
+      the [`'uncaughtException'`][] event.
+      The `'unhandled'` value may or may not be desirable in situations
+      where the `REPLServer` instance has been closed, depending on the particular
+      use case.
 * Returns: {repl.REPLServer}
 
 The `repl.start()` method creates and starts a [`repl.REPLServer`][] instance.
diff --git a/lib/repl.js b/lib/repl.js
index e747cc581cc8eb..779740bfd411ad 100644
--- a/lib/repl.js
+++ b/lib/repl.js
@@ -125,6 +125,7 @@ const {
     ERR_INVALID_ARG_VALUE,
     ERR_INVALID_REPL_EVAL_CONFIG,
     ERR_INVALID_REPL_INPUT,
+    ERR_INVALID_STATE,
     ERR_MISSING_ARGS,
     ERR_SCRIPT_EXECUTION_INTERRUPTED,
   },
@@ -195,14 +196,9 @@ function setupExceptionCapture() {
 
   process.addUncaughtExceptionCaptureCallback((err) => {
     const store = replContext.getStore();
-    // TODO(addaleax): Add back a `store.replServer.closed` check here
-    // as a semver-major change.
-    // This check may need to allow for an opt-out, since the change in
-    // behavior could lead to DoS vulnerabilities (e.g. in the case of
-    // the net-based REPL described in our docs).
     if (store?.replServer) {
-      store.replServer._handleError(err);
-      return true; // We handled it
+      const result = store.replServer._handleError(err);
+      return result !== 'unhandled'; // We handled it
     }
     // No active REPL context - let other handlers try
   });
@@ -387,6 +383,7 @@ class REPLServer extends Interface {
     this.lastError = undefined;
     this.breakEvalOnSigint = !!options.breakEvalOnSigint;
     this.editorMode = false;
+    this._userErrorHandler = options.handleError;
     // Context id for use with the inspector protocol.
     this[kContextId] = undefined;
     this[kLastCommandErrored] = false;
@@ -987,6 +984,20 @@ class REPLServer extends Interface {
   }
   _handleError(e) {
     debug('handle error');
+    if (this._userErrorHandler) {
+      const state = this._userErrorHandler(e);
+      if (state !== 'ignore' && state !== 'print' && state !== 'unhandled') {
+        throw new ERR_INVALID_STATE(
+          'External REPL error handler must return either "ignore", "print"' +
+          `, or "unhandled", but received: ${state}`);
+      }
+      if (state === 'ignore') {
+        return;
+      }
+      if (state === 'unhandled') {
+        return 'unhandled';
+      }
+    }
     let errStack = '';
 
     if (typeof e === 'object' && e !== null) {
diff --git a/test/parallel/test-repl-user-error-handler.js b/test/parallel/test-repl-user-error-handler.js
new file mode 100644
index 00000000000000..31bd46b13d36d1
--- /dev/null
+++ b/test/parallel/test-repl-user-error-handler.js
@@ -0,0 +1,84 @@
+'use strict';
+const common = require('../common');
+const { start } = require('node:repl');
+const assert = require('node:assert');
+const { PassThrough } = require('node:stream');
+const { once } = require('node:events');
+const test = require('node:test');
+const { spawn } = require('node:child_process');
+
+function* generateCases() {
+  for (const async of [false, true]) {
+    for (const handleErrorReturn of ['ignore', 'print', 'unhandled', 'badvalue']) {
+      if (handleErrorReturn === 'badvalue' && async) {
+        // Handled through a separate test using a child process
+        continue;
+      }
+      yield { async, handleErrorReturn };
+    }
+  }
+}
+
+for (const { async, handleErrorReturn } of generateCases()) {
+  test(`async: ${async}, handleErrorReturn: ${handleErrorReturn}`, async () => {
+    let err;
+    const options = {
+      input: new PassThrough(),
+      output: new PassThrough().setEncoding('utf8'),
+      handleError: common.mustCall((e) => {
+        err = e;
+        queueMicrotask(() => repl.emit('handled-error'));
+        return handleErrorReturn;
+      })
+    };
+
+    let uncaughtExceptionEvent;
+    if (handleErrorReturn === 'unhandled' && async) {
+      process.removeAllListeners('uncaughtException'); // Remove the test runner's handler
+      uncaughtExceptionEvent = once(process, 'uncaughtException');
+    }
+
+    const repl = start(options);
+    const inputString = async ?
+      'setImmediate(() => { throw new Error("testerror") })\n42\n' :
+      'throw new Error("testerror")\n42\n';
+    if (handleErrorReturn === 'badvalue') {
+      assert.throws(() => options.input.end(inputString), /ERR_INVALID_STATE/);
+      return;
+    }
+    options.input.end(inputString);
+
+    await once(repl, 'handled-error');
+    assert.strictEqual(err.message, 'testerror');
+    const outputString = options.output.read();
+    assert.match(outputString, /42/);
+
+    if (handleErrorReturn === 'print') {
+      assert.match(outputString, /testerror/);
+    } else {
+      assert.doesNotMatch(outputString, /testerror/);
+    }
+
+    if (uncaughtExceptionEvent) {
+      const [uncaughtErr] = await uncaughtExceptionEvent;
+      assert.strictEqual(uncaughtErr, err);
+    }
+  });
+}
+
+test('async: true, handleErrorReturn: badvalue', async () => {
+  // Can't test this the same way as the other combinations
+  // since this will take the process down in a way that
+  // cannot be caught.
+  const proc = spawn(process.execPath, ['-e', `
+    require('node:repl').start({
+      handleError: () => 'badvalue'
+    })
+  `], { encoding: 'utf8', stdio: 'pipe' });
+  proc.stdin.end('throw new Error("foo");');
+  let stderr = '';
+  proc.stderr.setEncoding('utf8').on('data', (data) => stderr += data);
+  const [exit] = await once(proc, 'close');
+  assert.strictEqual(exit, 1);
+  assert.match(stderr, /ERR_INVALID_STATE.+badvalue/);
+});