The efficient computation of period integrals for families of Calabi-Yau manifolds plays a central role for many applications in string compactifications. A very useful tool for this aim is given by the corresponding Picard-Fuchs differential ideals.

Existing methods to compute Picard-Fuchs ideals are usually limited to Calabi-Yau families with a moderat number of complex structure moduli. Based on a "guessing method", we systematically compute Picard-Fuchs ideals for Calabi-Yau threefolds which are hypersurfaces of toric varieties. Examining this large class of examples, we conjecture general properties of Picard-Fuchs ideals which might lead to a deeper understanding of the moduli space geometry of Calabi-Yau threefolds.