The cosmic microwave background (CMB) dipole, measured in the heliocentric frame, is conventionally attributed entirely to a local Lorentz boost. However, recent work [1] suggests the CMB dipole may have a non-kinematic component arising from local expansion gradients in space, or relativistic differential expansion. In this thesis we examine the possibility of a non-kinematic dipole component using exact inhomogeneous cosmological models that naturally give rise to this notion of differential expansion. In particular, we investigate the spherically symmetric Lemaître-Tolman-Bondi (LTB) model describing a local void and a less symmetric Szekeres model describing both a void and a neighbouring overdense structure. We derive analytic formulae to estimate the non-kinematic dipole and find a non-kinematic component of -0:12 ± 0:22 mK. As yet, a precise determination of a non-zero non-kinematic dipole is not possible given current measurements of the boost velocity of the heliocentric frame relative to the Local Group (LG) frame. We further characterise the extent to which observers in a local void, described by the LTB model, will see secondary effects attributed to a Lorentz boost, namely the aberration and modulation effects. We find that similar effects do arise for observers in the LTB model and therefore such effects are not unique to a Lorentz boost.