Log archiving will move the logs from one location to another and, optionally, zip them. We archive our zipped logs daily at midnight to another drive. These are stored then there are clean-up actions that run to delete files older than the retention requirements. The clean up actions run daily, typically around 6am.
For example, our host logs are archived daily, then deleted after 30 days. When archiving we prepend the ISO date to the hostname(2016-10-17-hostname.txt). Our catchall logs are also archived daily and then deleted after 6 months from the archive location.
We only use log rotation based on size. We limit each file to 250mb then rotate to a new file. This keeps the file size manageable when needing to open and search.