What the world knows today as Greek music usually has a bouzouki or two, and it is therefore difficult to make it sound convincing on the piano. This music has its origins in Rembetika. What is Rembetika?

Rembetika, Rebetiko, Rebetika - I've heard the Greeks use all these different words, originated in the takedhes, the hash dens of Anatolia, before the Greeks were chucked out of Turkey by Ataturk and the population exchanges took place in 1922/23. The rebetes were penniless musicians who often had lost their entire way of life in Anatolia, and they created what has been called the Greek blues.
For anyone interested in music, and social history, Rembetika is very important and very interesting. I recommend as an introduction, a potted history, and some of the best Rembetika around, Matt Barrett's website: