Notes on iPhone and iCloud, but not on Mac's Notes

I have notes that I've created on my iPhone and they've all been created under one account, my iCloud account. I can see all the notes when I go to iCloud.com but I can't access them when I open the Notes application on my Mac. I only see a select few of the notes from iPhone/iCloud.com on the Notes application on my Mac. How can I go about getting access to the rest of the notes from my Mac? And yes, I have iCloud set up on my Mac so I don't understand why this problem is occurring or how to fix it.