diff --git a/docs/kernel-patches.md b/docs/kernel-patches.md
index b773007ea..1b4b14a3c 100644
--- a/docs/kernel-patches.md
+++ b/docs/kernel-patches.md
@@ -4,7 +4,7 @@ We may apply patches to the Linux kernel used in Moby, primarily to
 cherry-pick some upstream patches or to add some additional
 functionality, not yet accepted upstream.
 
-Patches are located in `alpine/kernel/patches-<kernel version>` and should follow these rules:
+Patches are located in `kernel/patches-<kernel version>` and should follow these rules:
 - Patches *must* be in `git am` format, i.e. they should contain a
   complete and sensible commit message.
 - Patches *must* contain a Developer's Certificate of Origin.
@@ -87,7 +87,7 @@ Origin: https://patchwork.ozlabs.org/patch/622404/
 To export patches to Moby, you should use `git format-patch` from the Linux tree, e.g., something along these lines:
 ```sh
 cd $LINUXSRC
-rm $MOBYSRC/alpine/kernel/patches-4.9/*
+rm $MOBYSRC/kernel/patches-4.9/*
 git format-patch -o $MOBYSRC/kernel/patches-4.9 v4.9.15..HEAD
 ```
 
diff --git a/kernel/README.md b/kernel/README.md
index cd83a8c7b..3375cc401 100644
--- a/kernel/README.md
+++ b/kernel/README.md
@@ -1,12 +1,18 @@
-Temporary non modular kernel config for pinata alpha
+Linux kernel builds, based on mostly-vanilla upstream Linux kernels.
+See [../docs/kernel-patches.md] for how the local patches in `patches-*`
+are maintained.
 
-TODO: build with Alpine and/or use Alpine kernels - needs some patches.
-
-The build is mostly silent. To view the output use `docker log -f <containerid>`. The build creates multiple containers, so multiple
-invocations may be necessary. To view the full build output one may also invoke `docker build .` and then copy the build artefacts from the image afterwards.
+The build is mostly silent. A local build can be run via `make`. To view
+the output use `docker log -f <containerid>`. The build creates multiple
+containers, so multiple invocations may be necessary. To view the full build
+output one may also invoke `docker build .` and then copy the build artefacts
+from the image afterwards.
 
 To build with various debug options enabled, build the kernel with
-`make DEBUG=1`. The options enabled are listed in `kernel_config.debug`. This allocates a significant amount of memory on boot and you may need to adjust the kernel config on some systems. Specifically:
+`make DEBUG=1`. The options enabled are listed in `kernel_config.debug`.
+This allocates a significant amount of memory on boot and you may need to
+adjust the kernel config on some systems. Specifically:
+
 ```diff
 --- a/alpine/kernel/kernel_config
 +++ b/alpine/kernel/kernel_config