By a Calabi-Yau threefold I mean a simply connected compact Kahler threefold with trivial canonical bundle.

By an algebraic compact complex manifold, I mean one that admits a closed immersion into a complex projective space.

What are examples of non-algebraic Calabi-Yau threefolds? Or is there none?

What I know: if the Calabi-Yau threefold $ M $ has $ h^{2,0} (M) = 0 $, then it is algebraic. (Algebraicity holds for any compact Kahler manifold with the vanishing condition, btw). So any such example must have nonzero $ h^{2,0} $.

I don't know the Ricci flow viewpoint to this subject, so I'm probably missing something but I'm eager to learn.