The choice of CAT tools running on Linux has grown considerably over the last eight years. The breakthrough came in 2002, which saw the arrival of both OmegaT and Crossover Office (since rebranded Crossover Linux). OmegaT enjoyed steady adoption, eventually becoming the first (and so far only) open-source CAT tool in widespread use, and also a model project in its combination of user community involvement and scale of adoption. (Most open-source software projects are either driven by technophiles, or have significant commercial backing.) At the same time, Crossover Office enabled certain Microsoft CAT tools, notably Wordfast, to run on Linux.
This situation set the pattern for future developments. The ten or so Linux CAT tools suitable for use by mainstream professional translators are all without exception tools that also run on Windows. This can easily be explained by the Linux CAT tool market's size; it is much more worthwhile investing in development of software that can also tap into the huge market of Windows (and Mac) users.
Consequently, Java, with its "Write Once, Run Anywhere" philosophy, features prominently among the CAT tools for Linux. Tools written in Java include OmegaT, Heartsome, Swordfish, Wordfast Professional and Cafetran. Two other cross-platform languages are python and tcl/tk; these have produced Transolution and Esperantilo respectively.
The Crossover Office emulation layer not only brought Microsoft Word to the Linux desktop, but also several CAT tools written in Word's macro language and using Word as their user interface. These included Wordfisher and Sprint, development of which has now long been abandoned, but notably also Wordfast (now known as Wordfast Classic, to distingish it from the standalone "Professional" version).
For more details of the individual CAT tools/translation memory systems, select the product concerned from the menu on the left.