Magnetic fields permeate the entire universe, extending from the smallest to the largest observable length scales. A popular explanation for the origin ofthe magnetic fields observed in galaxies, clusters of galaxies, and the intergalactic medium is that seed fields generated due to quantum fluctuations inthe primordial universe are amplified later by astrophysical processes. According to the standard paradigm of magnetogenesis, the seed magnetic fieldson cosmological scales are generated during inflation by breaking the conformal invariance of the standard electromagnetic action. This is usuallyachieved through a non-conformal coupling of the electromagnetic field to the scalar field that drives inflation. Also, a parity violating term is oftenadded to the action to generate helical magnetic fields. I will begin the talk with a brief introduction to the essential idea of inflation. Thereafter, I willfirst discuss the effects of deviations from slow roll inflation on the spectra of non-helical as well as helical electromagnetic fields over large and smallscales in single field models of inflation. We find that, to generate nearly scale invariant spectra of magnetic fields, even in slow roll inflation, one has toconstruct non-conformal coupling functions that are dependent on the inflationary model being considered. We show that sharp features in the scalarpower spectrum generated due to departures from slow roll inflation inevitably lead to strong features in the power spectra of the electromagneticfields. Moreover, we find that such effects can also considerably suppress the strengths of the generated electromagnetic fields over the scales ofcosmological interest. While it seems possible to undo the strong features that arise in the electromagnetic power spectra in such situations, we pointout that it is realized at the cost of severely fine-tuned non-conformal coupling functions. To circumvent the challenges that arise in single field models,in the second part of the talk, I will discuss the generation of magnetic fields in two field models of inflation. We illustrate that, in two field models, withsuitably chosen non-conformal coupling functions, we can obtain spectra of magnetic fields of the required strength and shape even in situationsinvolving strong departures from slow roll. I will also discuss the imprints of the primordial magnetic fields generated in certain two field models on theanisotropies in the cosmic microwave background. In the third and final part, I will describe the evolution of the quantum state associated with theFourier modes of the electromagnetic field during inflation. We will track the evolution of the state using measures such as the Wigner ellipse,squeezing amplitude and quantum discord. Specifically, w e will show that the violation of parity leads to an enhancement of the squeezing amplitudeand the quantum discord associated with one of the two states of polarization. I will conclude the talk with a short summary and outlook. The talk willbe based on the following publications: 1. S. Tripathy, D. Chowdhury, R. K. Jain and L. Sriramkumar, Challenges in the choice of the non-conformalcoupling function in inflationary magnetogenesis, Phys. Rev. D 105, 063519 (2022) [arXiv:2111.01478 [astro-ph.CO]]. 2. S. Tripathy, D. Chowdhury, H.V. Ragavendra, R. K. Jain and L. Sriramkumar, Circumventing the challenges in the choice of the non-conformal coupling function in inflationarymagnetogenesis, Phys. Rev. D 107, 043501 (2023) [arXiv:2211.05834 [astro-ph.CO]]. 3. S. Tripathy, R. N. Raveendran, K. Parattu and L. Sriramkumar,Amplifying quantum discord during inflationary magnetogenesis through violation of parity, Phys. Rev. D 108, 123512 (2023) [arXiv:2306.16168 [gr-qc]].