Until Hubspot team have not implemented export of engagements you can export email messages & notes into CSV using a third-party solution - Import2 Wizard.
The steps to do that are pretty straightforward:
- Start a new export by selecting the tool to export from (Hubspot), and the type of records you want to export (emails, notes etc)
- Download the data to CSV (you have the option of filtering and choosing which fields to include in the export in this step if you wish).
You can watch a quick video here on how it works: https://youtu.be/1PNYXeavYac
Unfortunately, Import2 Wizard is not supporting image attachments export yet, however, I have passed the request to our tech team so this feature is added to the roadmap now.