If you want to run glibc programs in Alpine Linux, there are a few ways of doing so. You can install the gcompat compatibility layer, you can install glibc alongside musl (manually, as it isn't packaged), or you could do it the easy way and use either Flatpak (the easiest) or a chroot.

Because there are different use cases, this is just a slight overview about what's possible and what's sensible.

Your options

gcompat

gcompat is the go-to compatibility layer for Alpine users.

apk add gcompat

After that you run your binaries as normal.

Flatpak

Flatpak is by far the easiest method of running any graphical glibc program on Alpine. Firstly install it.

doas apk add flatpak

Then you can run any Flatpak application:

flatpak run <flatpak name>

It is recommended to enable Flathub using its instructions here, as most glibc programs you might need will be packaged there.

You can then install applications from it, for example:

flatpak install com.valvesoftware.Steam

Chroot

An option that's easier to generalize to other glibc applications is installing a glibc-based distribution into a chroot. You can then either chroot into it, or use a symlink and some configuration to make its glibc (and associated libraries) usable from Alpine.

After setting up a chroot using any of the methods described below, the loader can be set up in Alpine like so (these instructions are for a Debian chroot in /var/chroots/debian, on x86_64, but can be adapted to other systems by using the appropriate paths):

mkdir -p /lib64
ln -s /var/chroots/debian/lib/x86_64-linux-gnu/ld-2.33.so /lib64
printf '/var/chroots/debian/lib/x86_64-linux/gnu\n/var/chroots/debian/usr/lib/x86_64-linux-gnu\n' > /etc/ld.so.conf
/var/chroots/debian/sbin/ldconfig

Gentoo Linux

Select a stage3 from here and portage latest from here at gentoo/snapshots/portage-latest.tar.xz.

First,

sudo apk add xz

Enter the chroot:

mkdir ~/chroot
cd ~/chroot
tar -xvf stage3-*.tar.xz
tar -xvf portage-latest.tar.xz
mv portage usr
sudo mount --bind /dev dev
sudo mount --bind /sys sys
sudo mount -t proc proc proc
cp /etc/resolv.conf etc
sudo chroot . /bin/bash

And voilà, you have your working Gentoo chroot!

You can now take a look at Gentoo's Handbook to find out how you can configure and install your system, or simply extract/copy the program you need to run in your chroot enviroment and execute it.

Here is a wrapper script that is similar to arch-chroot when you frequently reuse this chroot:

Also, create an account with the same user name as host current user to the chroot or make changes to the userspec option to chroot line.

Contents of gentoo-chroot.sh

!/bin/bash
CHROOT_PATH="/home/$USER/chroot"
cd $CHROOT_PATH
mount | grep $CHROOT_PATH/dev || sudo mount --bind /dev dev
mount | grep $CHROOT_PATH/sys || sudo mount --bind /sys sys
mount | grep $CHROOT_PATH/proc || sudo mount -t proc proc proc
cp /etc/resolv.conf etc
sudo chroot --userspec=$USER:users . /bin/bash
echo "You must manually unmount $CHROOT_PATH/dev, $CHROOT_PATH/sys, $CHROOT_PATH/proc."

Do at chmod +x gentoo-chroot.sh to get it to work.

Arch Linux

Either use pacstrap (included with the arch-install-scripts package) or an Arch bootstrap image:

 sudo apk add arch-install-scripts
 mkdir ~/chroot && cd ~/chroot
 curl -O https://mirrors.edge.kernel.org/archlinux/iso/latest/archlinux-bootstrap-2021.04.01-x86_64.tar.gz^{[Dead Link]}
 sudo tar xzf archlinux-bootstrap-2021.04.01-x86_64.tar.gz && rm archlinux-bootstrap-2021.04.01-x86_64.tar.gz
 sudo sed -i '/evowise/s/^#//' root.x86_64/etc/pacman.d/mirrorlist
 sudo sed -i '/CheckSpace/s/^/#/' root.x86_64/etc/pacman.conf
 sudo arch-chroot root.x86_64
 [chroot]# pacman-key --init
 [chroot]# pacman-key --populate archlinux

Once that is done, update the system and install the desired package(s) (denoted by "foo" in this example):

 [chroot]# pacman -Syu foo

Debian

Use the provided debootstrap package to create the Debian chroot. --arch is optional, depending of your needs.

On the linux-grsec kernel, you will need to relax chroot limitations:

 sudo apk add debootstrap
 for i in /proc/sys/kernel/grsecurity/chroot_*; do echo 0 | sudo tee $i; done
 mkdir ~/chroot
 sudo debootstrap --arch=i386 wheezy ~/chroot http://http.debian.net/debian/
 for i in /proc/sys/kernel/grsecurity/chroot_*; do echo 1 | sudo tee $i; done
 sudo chroot ~/chroot /bin/bash

You can now use apt-get to install needed packages.