This question is too broad one. But one quick check that you can perform would be Go to
System > Configuration > Advanced > Advanced and verify that
Mage_Review model is in enabled state.
If that is not enabled state, then you should enable it.Otherwise that is the module that you should dig into in order to trace the issue.
Ok then start digging. I will help you with the first step. Rest you should do. When submitting a new product review, this is what executing in Magento by default.
So do a test review and dig from here. Stop until find the problem.
Note: The above case only help, if you have problem with storing reviews in database. If reviews are storing perfectly, then you should look into the admin section. So do a test review and look into the tables whether entry is present there or not. Tables associated with
Mage_Review module are review, review_detail, review_status, review_entity, review_entity_summary, review_store.