This article mentions the Ham Shack aboard the ISS. From the picture it looks like a small very light rig like a Yaesu FT-817. What radio(s) do the astronauts use when they talk to Hams and School-age kids (with help from licensed hams) on earth?
According to Wikipedia and ISSFANCLUB, in 2011, they had a Kenwood TM-D700 UHF/VHF rig, and also an Ericcson UHF/VHF rig. When the Kenwood had problems, they switched for a while to the Ericcson backup unit.
The official ARISS web site documents the current equipment as follows (scroll down for the headline Radios, Modes and Antennas on the ISS):
The ISS amateur radios are Ericsson MP-X handheld radios, a Kenwood TM D700 and a Kenwood D710.
The crew is currently able to use these radios to operate on the 2 m and 70 cm bands. Voice, packet radio and SSTV are the operational modes.
There is also a brand new "Ham Video" DVB-S digital television transmitter for the 2.4 GHz amateur radio band. The transmitter is being taken into use right now (July 2014) according the news page of the official site.