sageRegina
sageRegina is a packaging of the triangulation software regina making its installation under Sage as easy as typing the following command into a terminal:
sage pip install sageRegina log reginaInstall.log
This will retrieve regina from pypi and compile it in one to several hours and install it into a subdirectory of the one that sage is installed in. Regina is now ready to be used inside sage. Just start sage and type, for example:
sage: import regina
sage: t = regina.Example3.figureEight()
sage: print t.homology()
Z
sageRegina only requires a working sage installation and, on Mac OS X, the xcode command line tools. All libraries that regina depends on are either part of sage or included in sageRegina. sageRegina does not provide regina's GUI. Its installation is modeled after that of SnapPy. The license of regina applies.
Remarks:

Mac users only: Read this workaround if you get TLS/SSL related errors.

If you installed sageRegina before it was moved to PyPI (September 25, 2016), it is recommended to do an uninstall first, since the version numbering has slightly changed.

If you previously installed sageRegina and want to upgrade to a newer version, add upgrade after install to the above command line. You can also use upgrade to "downgrade" to a specific version, e.g., sage pip install upgrade sageRegina==5.0 (see versions).

You might need to give the (full) path to sage, either because your system cannot find sage (or because you want to install sageRegina in your own copy of sage when there is also a systemwide installed sage).
For example, on Mac OS X, you might need to type /Applications/SageMath8.0.app/sage.

Writing to the directory where sage is installed might require super user/administrator privileges. In this case, you need to prefix the installation command by sudo.

Alternatively, you can instead add user to the installation command so that regina will be installed as a user site package in your home directory instead.
How do I test that the installation worked?
You can check that sage is picking up the intended version and not an old one by typing inside sage
sage: import regina.sageRegina; regina.sageRegina.version
You can also run the python part of regina's testsuite by typing
sage: import regina.sageRegina; regina.sageRegina.runTests()
How do I install the xcode command line tools (Mac OS X)?
xcode is available for free through the AppStore. Once you have installed xcode, type the following to make the xcode command line tools available:
xcodeselect install
Please report the results if you tried it out on other platforms to Matthias Goerner (enischte at gmail dot com).

Mac OS X

Version 10.12.6 (Sierra)

Version 10.12.1 (Sierra)

Version 10.11.6 (El Capitan)

Version 10.11.3 (El Capitan)

Sage 7.1.beta3: ok

Sage 6.10: ok

Linux

Ubuntu 16.04

Sage 7.4: fail: Sage 7.4 Linux binaries just fundamentally broken for some Intel processors.

Sage 7.3: ok

RHEL 6

Sage 7.2 (compiled from source): ok: tested on Scientific Linux release 6.8, compiled with sage's own gcc 4.9
Older OS versions
In case the installation did not work...
Check whether the error you found is described on the troubleshooting page.
If not, please send an email to Matthias Goerner (enischte at gmail dot com) that includes the reginaInstall.log file and basic information about your system returned by the commands:
uname a
sage version
sage sh c "which gcc; gcc version"
sage sh c "which as; echo  as version"
If this is an issue with regina itself, rather the install script of sageRegina, please contact the original authors.
Where can I find the source code for sageRegina?
Here is the source code for the python packaging and for
regina.