Renewal Status & Process
It all depends on how your organisation works and how strict the rules are. One could argue that all memberships are renewed at the end of the year and payments are created but with status pending. A member could still benefit altough they did not pay. This means that the membership status should stay active,

One could also argue that as long as someone did not paid the member has no benefit in that case you want an inactive status come into play.

What is really cool about CiviCRM is that it is possible to define those membership status rules yourself. You can do that under Administer --> CiviMember --> Membership status rules.