We will discuss various aspects of the manifold of conformal field theories. Most of the time will be devoted to a review of older background material. It will allow us to give a unified and more conceptual treatment of some recent results. Background reading: H. Jockers, V. Kumar, J. M. Lapan, D. R. Morrison and M. Romo, “Two-Sphere Partition Functions and Gromov-Witten Invariants,” Commun. Math. Phys. 325, 1139 (2014). [arXiv:1208.6244 [hep-th]] http://arxiv.org/pdf/1208.6244v3.pdf J. Gomis and S. Lee, “Exact Kahler Potential from Gauge Theory and Mirror Symmetry,” JHEP 1304, 019 (2013). [arXiv:1210.6022 [hep-th]]. http://arxiv.org/pdf/1210.6022v2.pdf E. Gerchkovitz, J. Gomis and Z. Komargodski, “Sphere Partition Functions and the Zamolodchikov Metric,” JHEP 1411, 001 (2014). [arXiv:1405.7271 [hep-th]]. http://arxiv.org/pdf/1405.7271v2.pdf J. Gomis, P.- S. Hsin, Z. Komargodski, A. Schwimmer, N. Seiberg and S. Theisen, ``Anomalies, Conformal Manifolds, and Spheres,'' [arXiv:1509.08511 [hep-th]]. http://arxiv.org/pdf/1509.08511.pdf