Turbulence in magnetised plasmas is driven by microinstabilities which exist at the spatial scales of the ion and the electron thermal gyroradii, with time scales corresponding to the ion and the electron thermal speeds, respectively. Hence, plasma turbulence can have a well-separated long wavelength "ion scale" (IS) and short wavelength "electron scale" (ES), where the separation is controlled by the electron-to-deuterium mass ratio (me=mi)^1/2 1/60. Resolving multiscale plasma turbulence in direct numerical simulations (DNS) is costly due to the small value of (me/mi)^1/2; nonetheless, several DNS have been performed which show that interactions between the long wavelength and the short wavelength pieces of the turbulence can be important for determining the character of the turbulence. In this thesis we find scale-separated, coupled equations for the IS and the ES pieces of the turbulence, valid in the limit that (me/mi)^1/2 → 0. These equations can be efficiently simulated in a system of coupled flux tubes. The equations provide insight into the mechanisms and the impact of the cross-scale interactions between the IS and the ES pieces of the turbulence, whilst avoiding the cost of DNS. We find that to leading order the IS turbulence evolves independently of the ES turbulence. The ES turbulence is sheared by parallel variation in the IS E × B drift, and the drive of instability at the ES is modified by the gradient of the IS distribution function. We study the effect of IS turbulence on the linear stability of the electron temperature gradient (ETG) mode. We find that a strongly driven ETG instability is stabilised by strongly driven IS turbulence, but is only weakly suppressed by IS turbulence driven near marginal stability. We identify the dominant suppression mechanism as parallel-to-the-field shear in the IS E × B drift: the simple nature of this suppression mechanism may explain why short wavelength turbulence saturates at a low level in the presence of strongly driven long wavelength turbulence in DNS.