Abstract: Magnetic fields at all scales are prevalent in our universe. However, current cosmological models predict that initially the universe was bereft of large-scale fields. The standard equations of magnetohydrodynamics (MHD) do not permit magnetogenesis; in the MHD Faraday’s law, ∂_t B =∇×(V ×B ). Thus if B  is initially zero, it will remain zero for all time. A more accurate physical model is needed to explain the origins of magnetic fields observed today. I explore two velocity-driven mechanisms for magnetogenesis in 2-fluid plasma. The first is a novel kinematic ‘battery’ arising from convection of vorticity. A coupling between thermal and plasma oscillations, this classical mechanism can operate in flows that are incompressible, quasi-neural and barotropic. The second mechanism arises from inclusion of thermal effects in relativistic shear flow instabilities. In such flows, parallel perturbations are ubiquitously unstable at small scales, with growth rates reaching order ω_p for a defined range of parameter-space. I have also derived a general dispersion relation for three dimensional, warm, two species plasma with discontinuous shear flow, and will discuss the mathematics of relativistic plasma, sheared-flow instability and the Biermann battery.