The Andes is the longest mountain range in the world, stretching from tropical South America to austral Patagonia (12°N-55°S). Along with the climate differences associated with latitude, the Andean region also features contrasting slopes and elevations, reaching altitudes of more than 4,000 m. a.s.l., in a relatively narrow crosswise section, and hosts diverse ecosystems and human settlements. This complex landscape poses a great challenge to weather and climate simulations. The interaction of the topography with the large-scale atmospheric motions controls meteorological phenomena at scales of a few kilometers, often inadequately represented in global (grid spacing ∼200–50 km) and regional (∼50–25 km) climate simulations previously studied for the Andes. These simulations typically exhibit large biases in precipitation, wind and near-surface temperature over the Andes, and they are not suited to represent strong gradients associated with the regional processes. In recent years (∼2010–2024), a number of modeling studies, including convection permitting simulations, have contributed to our understanding of the characteristics and distribution of a variety of systems and processes along the Andes, including orographic precipitation, precipitation hotspots, mountain circulations, gravity waves, among others. This is Part I of a two-part review about atmospheric modeling over the Andes. In Part I we review the current strengths and limitations of numerical modeling in simulating key atmospheric-orographic processes for the weather and climate of the Andean region, including low-level jets, downslope winds, gravity waves, and orographic precipitation, among others. In Part II, we review how climate models simulate surface-atmosphere interactions and hydroclimate processes in the Andes Cordillera to offer information on projections for land-cover/land-use change or climate change. With a focus on the hydroclimate, we also address some of the main challenges in numerical modeling for the region.