diff --git a/src/lib.rs b/src/lib.rs
index 4d65ddf1b..53f1838ea 100644
--- a/src/lib.rs
+++ b/src/lib.rs
@@ -36,7 +36,11 @@ use dashmap::DashMap;
 use std::{
     convert::TryInto,
     fmt::Debug,
-    sync::{mpsc::SendError, Arc},
+    sync::{
+        atomic::{AtomicBool, Ordering},
+        mpsc::SendError,
+        Arc,
+    },
 };
 use tokio::runtime::Runtime;
 use tonic::codegen::http::uri::InvalidUri;
@@ -62,6 +66,13 @@ pub trait Core: Send + Sync {
 
     /// Returns an instance of ServerGateway.
     fn server_gateway(&self) -> Result<Arc<dyn ServerGatewayApis>>;
+
+    /// Eventually ceases all polling of the server. [Core::poll_task] should be called until it
+    /// returns [CoreError::ShuttingDown] to ensure that any workflows which are still undergoing
+    /// replay have an opportunity to finish. This means that the lang sdk will need to call
+    /// [Core::complete_task] for those workflows until they are done. At that point, the lang
+    /// SDK can end the process, or drop the [Core] instance, which will close the connection.
+    fn shutdown(&self) -> Result<()>;
 }
 
 /// Holds various configuration information required to call [init]
@@ -89,6 +100,7 @@ pub fn init(opts: CoreInitOptions) -> Result<impl Core> {
         workflow_machines: WorkflowConcurrencyManager::new(),
         workflow_task_tokens: Default::default(),
         pending_activations: Default::default(),
+        shutdown_requested: AtomicBool::new(false),
     })
 }
 
@@ -115,6 +127,9 @@ where
     /// Workflows that are currently under replay will queue their run ID here, indicating that
     /// there are more workflow tasks / activations to be performed.
     pending_activations: SegQueue<PendingActivation>,
+
+    /// Has shutdown been called?
+    shutdown_requested: AtomicBool,
 }
 
 #[derive(Debug)]
@@ -146,6 +161,10 @@ where
             });
         }
 
+        if self.shutdown_requested.load(Ordering::SeqCst) {
+            return Err(CoreError::ShuttingDown);
+        }
+
         // This will block forever in the event there is no work from the server
         let work = self
             .runtime
@@ -215,6 +234,11 @@ where
     fn server_gateway(&self) -> Result<Arc<dyn ServerGatewayApis>> {
         Ok(self.server_gateway.clone())
     }
+
+    fn shutdown(&self) -> Result<(), CoreError> {
+        self.shutdown_requested.store(true, Ordering::SeqCst);
+        Ok(())
+    }
 }
 
 impl<WP: ServerGatewayApis> CoreSDK<WP> {
@@ -271,8 +295,9 @@ impl<WP: ServerGatewayApis> CoreSDK<WP> {
 #[allow(clippy::large_enum_variant)]
 // NOTE: Docstrings take the place of #[error("xxxx")] here b/c of displaydoc
 pub enum CoreError {
-    /// No tasks to perform for now
-    NoWork,
+    /// [Core::shutdown] was called, and there are no more replay tasks to be handled. You must
+    /// call [Core::complete_task] for any remaining tasks, and then may exit.
+    ShuttingDown,
     /// Poll response from server was malformed: {0:?}
     BadDataFromWorkProvider(PollWorkflowTaskQueueResponse),
     /// Lang SDK sent us a malformed completion: {0:?}
@@ -302,6 +327,7 @@ pub enum CoreError {
 #[cfg(test)]
 mod test {
     use super::*;
+    use crate::machines::test_help::FakeCore;
     use crate::{
         machines::test_help::{build_fake_core, TestHistoryBuilder},
         protos::{
@@ -317,6 +343,7 @@ mod test {
             },
         },
     };
+    use rstest::{fixture, rstest};
 
     #[test]
     fn single_timer_test_across_wf_bridge() {
@@ -484,11 +511,8 @@ mod test {
         .unwrap();
     }
 
-    #[test]
-    fn single_timer_whole_replay_test_across_wf_bridge() {
-        let s = span!(Level::DEBUG, "Test start", t = "bridge");
-        let _enter = s.enter();
-
+    #[fixture]
+    fn single_timer_whole_replay() -> FakeCore {
         let wfid = "fake_wf_id";
         let run_id = "fake_run_id";
         let timer_1_id = "timer1".to_string();
@@ -543,5 +567,22 @@ mod test {
             task_tok,
         ))
         .unwrap();
+        core
+    }
+
+    #[rstest]
+    fn single_timer_whole_replay_test_across_wf_bridge(_single_timer_whole_replay: FakeCore) {
+        // Nothing to do here -- whole real test is in fixture. Rstest properly handles leading `_`
+    }
+
+    #[rstest]
+    fn after_shutdown_server_is_not_polled(single_timer_whole_replay: FakeCore) {
+        single_timer_whole_replay.shutdown().unwrap();
+        assert_matches!(
+            single_timer_whole_replay
+                .poll_task("irrelevant")
+                .unwrap_err(),
+            CoreError::ShuttingDown
+        );
     }
 }
diff --git a/src/machines/test_help/mod.rs b/src/machines/test_help/mod.rs
index f669750d9..9522ae745 100644
--- a/src/machines/test_help/mod.rs
+++ b/src/machines/test_help/mod.rs
@@ -17,9 +17,12 @@ use crate::{
     CoreSDK,
 };
 use rand::{thread_rng, Rng};
+use std::sync::atomic::AtomicBool;
 use std::{collections::VecDeque, sync::Arc};
 use tokio::runtime::Runtime;
 
+pub(crate) type FakeCore = CoreSDK<MockServerGateway>;
+
 /// Given identifiers for a workflow/run, and a test history builder, construct an instance of
 /// the core SDK with a mock server gateway that will produce the responses as appropriate.
 ///
@@ -31,7 +34,7 @@ pub(crate) fn build_fake_core(
     run_id: &str,
     t: &mut TestHistoryBuilder,
     response_batches: &[usize],
-) -> CoreSDK<MockServerGateway> {
+) -> FakeCore {
     let wf = Some(WorkflowExecution {
         workflow_id: wf_id.to_string(),
         run_id: run_id.to_string(),
@@ -69,5 +72,6 @@ pub(crate) fn build_fake_core(
         workflow_machines: WorkflowConcurrencyManager::new(),
         workflow_task_tokens: Default::default(),
         pending_activations: Default::default(),
+        shutdown_requested: AtomicBool::new(false),
     }
 }