How do renewals work? Why was no renewal invoice created?

Renewal invoices are created by the daily automation only when you turn it on, so check this first if no invoice appeared.

• Automatic: in Settings > Automation Settings > Invoicing & Reminders, turn on Create Renewal Invoices Automatically and set Generate Invoices This Many Days Ahead (above 0). Make sure the cron job is running (Automation Settings shows its status). Suspended services, services being cancelled, one-time and free services are skipped, and a period that already has an invoice is not invoiced again. Domains are invoiced the same way, that many days before they expire, when they are active and have Auto Renew on.
• Clients: turn on On-Demand Renewals in General Settings > Ordering and set the renewal window per billing cycle. Clients then see Renew now on the service page, which creates the renewal invoice.
• You: create an invoice from the client's page or Billings > Invoices > Create Invoice and move the next due date when it is paid.

Reminders, late fees, suspension and termination still run by themselves from the due date. Read Renewals.