Is there a way to sync mail on macbook with mail on iphone?

I have noticed a weird quirk and I'm not sure how to fix it. Certain email messages that are in mail on my macbook, don't ever show up on my iphone mail. I can't figure it out. I will go to access an email when I'm away from my computer and it simply isn't on my phone. I search for sender and it just isn't there, not in junk, etc. My phone receives emails regularly so it isn't that it can't get mail, it will just be random mail that I know I have, but cannot access. So strange. Is there a way to sync mail on my phone and mail on my mac? The last article I could find on this was several years old. Any help would be appreciated.