Root architecture is a critical factor in plant productivity, influencing how plants acquire water and nutrients from the soil. Root architecture refers to the spatial arrangement of root systems, encompassing the geometry and organization of root axes. It is distinct from root morphology, topology, and distribution, with architecture being the most comprehensive descriptor. Root architecture varies among species, genotypes, and even within individual root systems, and its complexity poses significant methodological challenges. Root architecture is vital for plant productivity because soil resources are unevenly distributed, and root systems must efficiently exploit these resources. Factors such as nutrient availability, water distribution, and soil pH create spatial and temporal gradients that influence root growth and resource acquisition. Root architecture determines how effectively a plant can explore the soil, respond to localized resource availability, and distribute resource capture and transport functions. Root architecture is influenced by various factors, including root exudates, symbiotic relationships with mycorrhizae and nitrogen-fixing bacteria, and environmental conditions. The efficiency of root architecture in acquiring resources is linked to the balance between resource investment and acquisition. For example, in common beans, P-efficient genotypes have highly branched root systems that enhance P uptake. Root architecture also affects mechanical support for the shoot and interactions with soil biota. Root architecture is studied in both agricultural and ecological contexts. In agriculture, root architecture influences P efficiency in beans, while in ecology, it affects water acquisition in desert succulents. Simulation models and imaging techniques like tomography are valuable tools for studying root architecture, despite the challenges of observing and quantifying it in situ. Fractal geometry offers a new approach to quantifying root architecture, providing insights into its complexity and functional significance. However, the physiological basis of root architecture remains poorly understood, with challenges in integrating the various processes that contribute to it. Research on root gravitropism, lateral branching, environmental plasticity, and root senescence is essential for advancing our understanding of root architecture and its role in plant productivity. A multidisciplinary approach is needed to address these challenges and improve our ability to predict and manage plant growth in diverse environments.Root architecture is a critical factor in plant productivity, influencing how plants acquire water and nutrients from the soil. Root architecture refers to the spatial arrangement of root systems, encompassing the geometry and organization of root axes. It is distinct from root morphology, topology, and distribution, with architecture being the most comprehensive descriptor. Root architecture varies among species, genotypes, and even within individual root systems, and its complexity poses significant methodological challenges. Root architecture is vital for plant productivity because soil resources are unevenly distributed, and root systems must efficiently exploit these resources. Factors such as nutrient availability, water distribution, and soil pH create spatial and temporal gradients that influence root growth and resource acquisition. Root architecture determines how effectively a plant can explore the soil, respond to localized resource availability, and distribute resource capture and transport functions. Root architecture is influenced by various factors, including root exudates, symbiotic relationships with mycorrhizae and nitrogen-fixing bacteria, and environmental conditions. The efficiency of root architecture in acquiring resources is linked to the balance between resource investment and acquisition. For example, in common beans, P-efficient genotypes have highly branched root systems that enhance P uptake. Root architecture also affects mechanical support for the shoot and interactions with soil biota. Root architecture is studied in both agricultural and ecological contexts. In agriculture, root architecture influences P efficiency in beans, while in ecology, it affects water acquisition in desert succulents. Simulation models and imaging techniques like tomography are valuable tools for studying root architecture, despite the challenges of observing and quantifying it in situ. Fractal geometry offers a new approach to quantifying root architecture, providing insights into its complexity and functional significance. However, the physiological basis of root architecture remains poorly understood, with challenges in integrating the various processes that contribute to it. Research on root gravitropism, lateral branching, environmental plasticity, and root senescence is essential for advancing our understanding of root architecture and its role in plant productivity. A multidisciplinary approach is needed to address these challenges and improve our ability to predict and manage plant growth in diverse environments.