Realistically, MVC is mostly a UI implementation pattern, so the question is somewhat moot. However, there are really only two big-picture options. Your controller typically dispatches requests to load or save entities in your model using either 1) a service layer of some kind or 2) the Active Record pattern.
The service layer can take any of a number of forms, though my personal preference is to work with a repository abstraction for the aggregate root entities, the concrete implementations of which will either work with some sort of ORM, or a lightweight DAO, or an API for some non-relational store if that makes sense for the application.
The Active Record pattern means that your model has responsibility for persistence, although it usually means a base class of some sort manages the mappings to your store, so your model is not really that directly involved.
Basically, the controller dispatches requests to persist objects, whether that's a call to your repository, your UnitOfWork implementation, or the Save method on your entities. If you're using repositories, your model objects are persistence-ignorant.