For your company's in-house and indirect expenses that are not project-specific, Core can track them as overheads. It is recommended that you create an internal overhead project and track all your overhead expenses against it. Typically, these expenses are not billable nor reimbursable.
Project-specific, direct expenses should be logged against their respective projects and made billable to the client. The client pays for these expenses.
In Core, we have reimbursable expenses, which should not be confused with the billable expenses (explained above). These 'Reimbursable' expenses are reimbursable to the employees. They might or might not be billable to the client.
There are many reports in Core that show project-specific expenses and company overhead expenses.