Odoo doesn't have a dedicated helpdesk module in CE. Enterprise has the Helpdesk module with SLA, automatic assignment, and customer portal. But in CE you can build solid ticket management with existing modules and a small custom module.
Enterprise Helpdesk
Kanban board with stages: New, In Progress, Waiting on Customer, Resolved, Closed. SLA rules: "First response within 4 hours, resolution within 24 hours." Automatic assignment based on team, competence, or round-robin. Customer portal where customers create and track tickets.
CE alternative
The project module with a dedicated "Support" project. Each ticket is a task. Stages match the support flow. Email alias: support@your-domain.com creates tasks automatically. Time tracking per ticket if you invoice support hours.
It lacks SLA automation and customer portal (in CE the portal doesn't have task visibility), but for internal support or low customer volume it works.
OCA modules
The OCA/helpdesk module (if available for your version) provides basic helpdesk functionality in CE. Check OCA GitHub for current status.
Email integration
Regardless of solution: configure an email alias that creates tickets automatically. Customer sends email, ticket is created, assignment happens (manually or automatically), reply is sent from Odoo. The entire conversation is logged. The customer never needs to log in if they don't want to.
Reports
Tickets per period, average resolution time, tickets per team and type. In Enterprise: built-in dashboards. In CE: pivot view and grouping on tasks gives basic statistics.
Support isn't about the tool. It's about the process. Define the flow, then choose the tool.