In recent years, the investigation of geometries of noncommutative tori has attracted attention from both mathematics and physics. In this talk, I will report on recent development in the study of different geometries on noncommutative tori and discuss a new family of metrics, called functional metrics, on noncommutative tori and the study of spectral invariants of geometric operators related to these metrics. My aim would be to show how some computational ideas gave us advantages, at least symbolically, in computing the invariants, among others the scalar curvature of these metrics. The talk is based on joint work with M. Khalkhali: arXiv:1811.04004 [math.QA].