You can find information on the progress of a civil case in a local court (Irinodikeio) / Court of First Instance / Appeal Court. You will need to select the court from the relevant list and enter the year, and either the GRN (General Registration Number) or the SRN (Special Registration Number) of the case.
If the document has been filed with the Court, the relevant entry will appear in the Documents section. By selecting the record and then clicking on the Details button, you will be transferred to a new screen with detailed information on each stage of the case.