Darling is to OS X programs as Wine is to Windows programs for running native binaries on Linux. Darling aimed to provide an ABI-compatible set of libraries/frameworks to those used on OS X. Darling leveraged some of GNUstep and other open-source projects for working out the Apple frameworks support on Linux. The developers working on Project Darling achieved some success in running unmodified OS X binaries on Linux.
My last update posted to Phoronix was in July of this year when saying Work Still Underway To Run OS X Binaries On Linux. Code was still happening for Project Darling through the summer, but for the past four months now there's been virtually no public activity around Darling.
Project Darling now hasn't seen any project Wiki changes since August. More pressing is that the Darling Git repository hasn't seen any new activity since September. The other related Darling repositories for a FUSE module for mounting DMG files on Linux and Mach API emulation for Linux also haven't seen any new activity in quite a while.
The lead developer, Luboš Doležel, seems to have moved on from the project. Luboš Doležel still is doing GitHub activity but now seems to be back to focusing upon his Fatrat project, a Linux download manager program written in Qt. At least for most Linux users, running OS X programs on Linux is not needed especially with there being Windows versions for many of the popular OS X programs where Wine likely does a much better job for non-Linux-native software.