Multi-loop Feynman integrals are crucial in meeting the requirements of collider experiments for high-precision theory predictions. In this talk I will discuss the central role that geometry plays in computing such integrals. Significant classes of geometries appearing in Feynman integral are elliptic curves and their natural generalizations, namely Calabi-Yau manifolds and higher genus curves. On the example of a simple class of Calabi-Yau integrals, the so-called Banana integrals, I will demonstrate how geometric information can be leveraged to evaluate Feynman integrals.