Inflation refers to a period of exponentially rapid expansion of the universe in the very early stages of the radiation dominated era. Bouncing scenarios correspond to situations wherein the universe undergoes a phase of contraction followed by an expanding era, with a bounce connecting the two epochs. In this talk, I shall compare and contrast between these two alternative scenarios of the early universe, both of which provide mechanisms for the generation of primordial scalar and tensor perturbations. By examining results at the level of two and three-point functions involving the scalar and the tensor perturbations, I shall describe the efforts underway towards arriving at observables that can, in principle, be made use of to discriminate between these alternative scenarios. Furthermore, I shall discuss the origin and evolution of primordial magnetic fields, which could act as seed fields for the large scale magnetic fields observed in the universe today. I shall also describe the characteristics of the cross-correlations between the primordial magnetic fields and scalar perturbations in bouncing universes, as well as the cross-correlations between the primordial helical magnetic fields and scalar perturbations in de Sitter inflation.