Log file
Log files store details about the run of Factorio and contain information that help when solving bugs. Log files exist from version 0.10.0.
Log File Location
Factorio keeps log files in the Application Directory, that is next to the saves and mods directories.
The file you need most of the time is factorio-current.log. Backup copy of the log file from previous run is in factorio-previous.log.
Bug Reporting
Log files are important for finding crashes, especially ones related to automatic updates and graphic settings. Please attach the current log file to all crash reports.
Privacy
Log files (in 0.10.5 and later) contain date and time of your Factorio session, your updater login name and full paths for some files belonging to Factorio or mods. Before 0.10.5 the log also could contain your updater token (not a password :-) ) as a part of update request URLs.