diff --git a/lib/container.sh b/lib/container.sh
index a952dad..1fe3f40 100644
--- a/lib/container.sh
+++ b/lib/container.sh
@@ -123,5 +123,84 @@ echo "→ Stopping \$CONTAINER_NAME..."
 STOP
     chmod +x "$project_dir/stop.sh"
 
-    success "Generated: start.sh  stop.sh  bin/claude"
+    # ── update.sh — update core, claude-code, and optionally OS packages ──
+    cat > "$project_dir/update.sh" <<UPDATE
+#!/usr/bin/env bash
+set -uo pipefail
+SCRIPT_DIR="\$(cd "\$(dirname "\${BASH_SOURCE[0]}")" && pwd)"
+PROJECT_DIR="\$SCRIPT_DIR"
+CONTAINER_NAME="${container_name}"
+IMAGE_NAME="${slug}"
+RUNTIME="\$(command -v podman || command -v docker || true)"
+CS_CORE="\${CS_CORE_DIR:-\$HOME/.context-studio/core}"
+
+GREEN='\033[0;32m'; CYAN='\033[0;36m'; YELLOW='\033[1;33m'; BOLD='\033[1m'; RESET='\033[0m'
+info()    { echo -e "\${CYAN}\${BOLD}[update]\${RESET} \$*"; }
+success() { echo -e "\${GREEN}\${BOLD}[ok]\${RESET}    \$*"; }
+warn()    { echo -e "\${YELLOW}\${BOLD}[warn]\${RESET}  \$*"; }
+
+CONTAINER_RUNNING=false
+if "\$RUNTIME" container inspect "\$CONTAINER_NAME" --format '{{.State.Running}}' 2>/dev/null | grep -q true; then
+    CONTAINER_RUNNING=true
+fi
+
+# ── 1. Update Context Studio Core ───────────────────────────────────────
+info "Updating Context Studio Core..."
+if [[ -d "\$CS_CORE/.git" ]]; then
+    git -C "\$CS_CORE" pull --ff-only && success "Core updated." || warn "Core pull failed — continuing with current version."
+else
+    warn "Core not found at \$CS_CORE — skipping."
+fi
+
+# ── 2. Update Claude Code in container ──────────────────────────────────
+info "Updating Claude Code (claude-code)..."
+if \$CONTAINER_RUNNING; then
+    "\$RUNTIME" exec "\$CONTAINER_NAME" npm install -g @anthropic-ai/claude-code \
+        && success "Claude Code updated in running container." \
+        || warn "Claude Code update failed."
+else
+    warn "Container not running — Claude Code will be updated on next image build."
+fi
+
+# ── 3. Update OS packages in container ──────────────────────────────────
+info "Updating OS packages in container..."
+if \$CONTAINER_RUNNING; then
+    "\$RUNTIME" exec "\$CONTAINER_NAME" bash -c "apt-get update -qq && apt-get upgrade -y" \
+        && success "OS packages updated in running container." \
+        || warn "OS package update failed."
+else
+    warn "Container not running — OS packages will be updated on next image build."
+fi
+
+# ── 4. Rebuild image to persist updates ─────────────────────────────────
+echo ""
+echo -e "\${BOLD}Rebuild container image?\${RESET}"
+echo -e "  Rebuilds from scratch with latest base image + all packages."
+echo -e "  ${YELLOW}⚠  Takes 5–15 minutes. Stops the running container.\${RESET}"
+echo -ne "Rebuild now? \${CYAN}[y/N]\${RESET}: "
+read -r _rebuild || true
+_rebuild="\${_rebuild:-n}"
+
+if [[ "\$_rebuild" =~ ^[Yy]\$ ]]; then
+    info "Stopping container..."
+    "\$RUNTIME" rm -f "\$CONTAINER_NAME" 2>/dev/null || true
+
+    info "Rebuilding image '\$IMAGE_NAME' (--pull --no-cache)..."
+    "\$RUNTIME" build --pull --no-cache -t "\$IMAGE_NAME" "\$PROJECT_DIR/.devcontainer/" \
+        && success "Image rebuilt. Run ./start.sh to start with the fresh image." \
+        || { echo "Image build failed." >&2; exit 1; }
+else
+    info "Skipped image rebuild."
+    if \$CONTAINER_RUNNING; then
+        warn "In-container updates are temporary — they will be lost when the container is recreated."
+        warn "Run ./update.sh again and choose 'y' to rebuild, or run ./start.sh (which recreates the container from the old image)."
+    fi
+fi
+
+echo ""
+success "Update complete."
+UPDATE
+    chmod +x "$project_dir/update.sh"
+
+    success "Generated: start.sh  stop.sh  update.sh  bin/claude"
 }
diff --git a/wizard.sh b/wizard.sh
index 6ec131d..48574fb 100755
--- a/wizard.sh
+++ b/wizard.sh
@@ -137,6 +137,11 @@ print_next_steps() {
     echo -e "${BOLD}Stop the container:${RESET}"
     echo -e "  ${CYAN}./stop.sh${RESET}"
     echo ""
+    echo -e "${BOLD}Update everything:${RESET}"
+    echo -e "  ${CYAN}./update.sh${RESET}"
+    echo -e "  Updates Context Studio Core, Claude Code, and OS packages."
+    echo -e "  Optionally rebuilds the image from scratch."
+    echo ""
     echo -e "${BOLD}How it works:${RESET}"
     echo -e "  • Context Studio Core runs on your host (Electron UI, no display issues)"
     echo -e "  • Claude Code agents run inside container ${CYAN}cs-${slug}${RESET}"