diff --git a/docs/k8s.rst b/docs/k8s.rst
index 087d93d..15130bb 100644
--- a/docs/k8s.rst
+++ b/docs/k8s.rst
@@ -57,7 +57,7 @@ Technical details
 
 Under the hood, Tutor wraps ``kubectl`` commands to interact with the cluster. The various commands called by Tutor are printed in the console, so that you can reproduce and modify them yourself.
 
-Basically, the whole platform is described in manifest files stored in ``$(tutor config printroot)/env/k8s``. There is also a ``kustomization.yml`` file at the project root for `declarative application management <https://kubectl.docs.kubernetes.io/pages/app_management/apply.html>`_. This allows us to start and update resources with commands similar to ``kubectl apply -k $(tutor config printroot) --selector=...`` (see the ``kubectl apply`` `official documentation <https://kubectl.docs.kubernetes.io/pages/app_management/apply.html>`_).
+Basically, the whole platform is described in manifest files stored in ``$(tutor config printroot)/env/k8s``. There is also a ``kustomization.yml`` file at the project root for `declarative application management <https://kubectl.docs.kubernetes.io/guides/config_management/introduction/#declarative-application-management>`__. This allows us to start and update resources with commands similar to ``kubectl apply -k $(tutor config printroot) --selector=...`` (see the ``kubectl apply`` `official documentation <https://kubectl.docs.kubernetes.io/references/kubectl/apply/>`__).
 
 The other benefit of ``kubectl apply`` is that it allows you to customise the Kubernetes resources as much as you want. For instance, the default Tutor configuration can be extended by a ``kustomization.yml`` file stored in ``$(tutor config printroot)/env-custom/`` and which would start with::
 
@@ -67,7 +67,7 @@ The other benefit of ``kubectl apply`` is that it allows you to customise the Ku
     - ../env/
     ...
 
-To learn more about "kustomizations", refer to the `official documentation <https://kubectl.docs.kubernetes.io/pages/app_customization/introduction.html>`__.
+To learn more about "kustomizations", refer to the `official documentation <https://kubectl.docs.kubernetes.io/references/kustomize/kustomization/>`__.
 
 Quickstart
 ----------
@@ -115,5 +115,3 @@ Updating docker images
 Kubernetes does not provide a single command for updating docker images out of the box. A `commonly used trick <https://github.com/kubernetes/kubernetes/issues/33664>`_ is to modify an innocuous label on all resources::
 
     kubectl patch -k "$(tutor config printroot)/env" --patch "{\"spec\": {\"template\": {\"metadata\": {\"labels\": {\"date\": \"`date +'%Y%m%d-%H%M%S'`\"}}}}}"
-
-