Odoo is an open source accounting software. With much more features than only accounting, such as warehouse management, project management, HR management etc.
CiviCRM is an open source software for non-profit and is great in membership management, donor management etc.
For one of our clients we have been working in integrating both CiviCRM and Odoo where Odoo is leading in the financial data and CiviCRM is leading in the contact and membership data.
Meaning that in CiviCRM we create memberships and memberships contributions. Those contributions are synced to Odoo as invoices. In Odoo the invoices marked as direct debits are exported and send to the bank and in Odoo we read and reconcile the bank statements and marking the invoices as paid. As soon as an invoice is marked as paid the contribution in CiviCRM is also marked as completed. In addition when an invoice is created in Odoo this invoice is also created as a contribution in CiviCRM.
The financial department could also remind people of unpaid contribution from within Odoo. This comminication with the members is logged as an activity in CiviCRM. So the membership department could see that the financial department has contacted this member about unpaid contributions.
At this moment the synchronisation between Odoo and CiviCRM is in a testing phase.