The eddy-covariance method is a tool that uses the high-frequency turbulent fluctuations within the atmosphere to determine energy and matter fluxes between the atmosphere and the underlying surface. The most important device is the sonic anemometer to measure the fluctuations of the three-component wind vectors, with the first instruments developed in the 1960s in Moscow and tested in the Volga steppe region. This paper presents a general overview on eddy-covariance methodology and instrumentation, including sophisticated updates based on wavelet analysis that help to overcome theoretical limitations with respect to investigating fluxes at high temporal resolution, and above large landscapes. As a first example for these updates, we present high-resolution methane fluxes in the Siberian permafrost area characterized by highly non-steady-state conditions. In a second example, we analyze aircraft measurements in the Lena region, which presents a horizontal distribution of the sensible heat fluxes from the surface to the boundary layer height, demonstrating the effect of the topography on the turbulent fluxes.