  Body tides reveal information about planetary interiors and affect their
evolution. Most models to compute body tides rely on the assumption of a
spherically-symmetric interior. However, several processes can lead to lateral
variations of interior properties. We present a new spectral method to compute
the tidal response of laterally-heterogeneous bodies. Compared to previous
spectral methods, our approach is not limited to small-amplitude lateral
variations; compared to finite element codes, the approach is more
computationally-efficient. While the tidal response of a spherically-symmetric
body has the same wave-length as the tidal force; lateral heterogeneities
produce an additional tidal response with an spectra that depends on the
spatial pattern of such variations. For Mercury, the Moon and Io the amplitude
of this signal is as high as $1\%-10\%$ the main tidal response for
long-wavelength shear modulus variations higher than $\sim 10\%$ the mean shear
modulus. For Europa, Ganymede and Enceladus, shell-thickness variations of
$50\%$ the mean shell thickness can cause an additional signal of $\sim 1\%$
and $\sim 10\%$ for the Jovian moons and Encelaudus, respectively. Future
missions, such as $ \textit{BepiColombo}$ and $\textit{JUICE}$, might measure
these signals. Lateral variations of viscosity affect the distribution of tidal
heating. This can drive the thermal evolution of tidally-active bodies and
affect the distribution of active regions.
