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The Atacama Large Millimeter/submillimeter Array (ALMA) offers new diagnosticpossibilities that complement other commonly used diagnostics for the study ofour Sun. In particular, ALMA's ability to serve as an essentially linearthermometer of the chromospheric gas at unprecedented spatial resolution atmillimetre wavelengths and future polarisation measurements have greatdiagnostic potential. Solar ALMA observations are therefore expected tocontribute significantly to answering long-standing questions about thestructure, dynamics and energy balance of the outer layers of the solaratmosphere. In this regard, current and future ALMA data are also important forconstraining and further developing numerical models of the solar atmosphere,which in turn are often vital for the interpretation of observations. Thelatter is particularly important given the Sun's highly intermittent anddynamic nature that involves a plethora of processes occurring over extendedranges in spatial and temporal scales. Realistic forward modelling of the Suntherefore requires time-dependent three-dimensional radiationmagnetohydrodynamics that account for non-equilibrium effects and, typically asa separate step, detailed radiative transfer calculations, resulting insynthetic observables that can be compared to observations. Such artificialobservations sometimes also account for instrumental and seeing effects, which,in addition to aiding the interpretation of observations, provide instructivetools for designing and optimising ALMA's solar observing modes. In the otherdirection, ALMA data in combination with other simultaneous observationsenables the reconstruction of the solar atmospheric structure via datainversion techniques. This article highlights central aspects of the impact ofALMA for numerical modelling for the Sun, their potential and challenges,together with selected examples.

Prospects and challenges of numerical modelling of the Sun at millimetre wavelengths