Update kernels documentation: add xeus, jupyter-client, ipykernel (#601)

* Update kernels documentation: add xeus, jupyter-client, ipykernel remove outdated info

* Update kernels.rst

* Cut ipyparallel and ipwidgets from kernels page as those are not kernels

* Apply suggestions from code review

Co-authored-by: Chris Holdgraf <choldgraf@gmail.com>

* Correct swapped ipython and ipykernel links

Co-authored-by: Chris Holdgraf <choldgraf@gmail.com>

docs/source/projects/kernels.rst

@@ -4,10 +4,9 @@
 Kernels (Programming Languages)
 ===============================
 
-The Jupyter team maintains the `IPython kernel <https://github.com/ipython/ipython>`_
-since the Jupyter notebook server depends on the IPython :term:`kernel`
-functionality. Many other languages, in addition to Python, may be used in
-the notebook.
+The Jupyter team maintains the `IPython <https://github.com/ipython/ipython>`_
+project which is shipped as a default kernel (as :term:`ipykernel`) in a number of Jupyter clients.
+Many other languages, in addition to Python, may be used in the notebook.
 
 The community maintains many other language kernels, and new kernels become
 available often. Please see the `list of available kernels`_ for additional
@@ -19,8 +18,18 @@ Kernels
 
 Kernels are `programming language specific` processes that run independently
 and interact with the Jupyter Applications and their user interfaces.
-`IPython <https://ipython.org>`__ is the reference Jupyter kernel, providing a
-powerful environment for interactive computing in Python.
+`ipykernel <https://github.com/ipython/ipykernel>`__ is the reference Jupyter kernel
+built on top of `IPython <https://ipython.org>`__,
+providing a powerful environment for interactive computing in Python.
+
+`jupyter-client <https://jupyter-client.readthedocs.io/en/stable/>`__ contains
+the authoritative description of the Jupyter messaging protocol which is used
+by clients to communicate with the kernels.
+
+`Xeus <https://xeus.readthedocs.io/en/latest/>`__ facilitates the
+implementation of kernels for Jupyter and provides a number of kernels such as
+`xeus-cling <https://github.com/jupyter-xeus/xeus-cling>`__ (C++),
+`xeus-sql <https://github.com/jupyter-xeus/xeus-sql>`__ (SQL) and many more.
 
 .. glossary::
 
@@ -29,19 +38,20 @@ powerful environment for interactive computing in Python.
         `Documentation <https://ipython.readthedocs.io/en/stable/>`__ |
         `Repo <https://github.com/ipython/ipython>`__
 
-    `ipywidgets <https://ipywidgets.readthedocs.io/en/latest/>`__
-        interactive widgets for Python in the Jupyter Notebook.
-        `Documentation <https://ipywidgets.readthedocs.io/en/latest/>`__ |
-        `Repo <https://github.com/ipython/ipywidgets>`__
+    `ipykernel <ipykernel>`__
+        the wrapper around IPython which enables using IPython as a kernel
+        `Repo <https://github.com/ipython/ipykernel>`__
 
-    `ipyparallel <https://ipyparallel.readthedocs.io/en/latest/>`__
-        lightweight parallel computing in Python offering seamless notebook integration.
-        `Documentation <https://ipyparallel.readthedocs.io/en/latest/>`__ |
-        `Repo <https://github.com/ipython/ipyparallel>`__
+    `Xeus <https://ipyparallel.readthedocs.io/en/latest/>`__
+        library facilitating the implementation of kernels for Jupyter.
+        It implements the Jupyter Kernel protocol so developers
+        can focus on implementing the interpreter part of the kernel.
+        `Documentation <https://xeus.readthedocs.io/en/latest/>`__ |
+        `Repo <https://github.com/jupyter-xeus/xeus>`__
 
 .. seealso::
 
-      `Jupyter kernels <https://github.com/ipython/ipython/wiki/IPython-kernels-for-other-languages>`_
+      `Jupyter kernels <list of available kernels_>`_
 
       A full list of kernels available for other languages. Many of
       these kernels are developed by third parties and may or may not be stable.