We have been developing software applications for "tiny" computer systems. Our particular focus has been on systems that support a full Linux OS. Linux is a very rich application environment that supports program development, graphical user interfaces, and a large variety of peripheral devices. Code is generally easily ported among systems of various sizes.
BeagleBone & BeagleBone Black. The BBB is the latest in the Beagle line. It sports a 1 GHz processor, a small footprint, and expandability via daughterboard "capes". The basic board has USB, Ethernet, and HDMI interfaces.
Beagleboard XM. This board has a comprehensive set of interfaces, including full stereo audio, Ethernet, USB, HDMI, etc. It is the platform we have used for the Remote Receiver Project (RRX) in support of the ARRL Club station, W1HQ.
Raspberry Pi. The original Pi (model A or B) is a less powerful, less expensive, but very popular board that still runs Linux and supports many of the same applications as the Beagleboard. The Raspberry Pi models 2 and 3 are more powerful!
Wikipedia has a List of single-board computers. "Single boardishness" is not the only criterion. Frequently, core CPU, RAM, and some I/O connectors are provided on a board, but additional daughter-boards (shields or capes) are stacked on the basic board to complete a compact system. Alternatively, peripherals are added via standard connections like USB.
Projects and Publications
Check out our Tiny Python Panadapter. See cover, QST, for January, 2014 (above) and April, 2014. It's a panadapter that accepts I/Q IF channels and displays power spectra and waterfall. Tested on Raspberry Pi, BeagleBone Black, and Linux PCs. Open source, of course!