The fiber product of certain rational elliptic surfaces over P1 were first studied by Schoen in the 80s to answer 
(negatively) questions from string theory. Over the decades  the  “Schoens”  have provided evidence for  
various conjectures as well as counterexamples to others. I will discuss  some of these conjectures, 
and conclude by revisiting the  quest for bounds of Calabi-Yau threefolds which motivated the original construction.