The agronomic sciences are those that are applied to soil and water management and crop production, including soil, water and plant sciences and related disciplines. The science of spatial and temporal water management includes many agronomic science factors, including soil physics, biophysics, plant responses to soil properties and weather, and the spatial and temporal variations of these. Irrigation practices have always afforded some degree of management in time and have inherently afforded management choices across the spaces defined by irrigation system structures and water delivery capacities. Recent advances in site-specific, variable-rate irrigation (SSVRI) using pressurized irrigation systems have, however, brought into play a greatly increased ability to manage water applications in time and space. Decision support systems appropriate to SSVRI management have, however, lagged behind due to gaps in knowledge and technology in three areas: (1) the science of plant responses to irrigation, chemigation and environment (both atmospheric and rhizospheric), (2) sensing systems effective for SSVRI management, and (3) algorithms and systems for SSVRI control. Science and technology in these three areas are inextricably linked through the agronomic sciences. In the realm of soil physics, both soil hydraulic characteristics and soil water content and potential measurement methods are relevant and will be discussed in view of recent advances in soil water measurement. Biophysical aspects include canopy temperature responses to microclimatic forcing factors and soil water status, which are tied to the surface energy balance, transpiration rate and plant turgor. Recent work on iterative solution of the soil and canopy energy balances to estimate canopy temperature is discussed in light of canopy temperature based irrigation scheduling algorithms such as the time-temperature threshold and the integrated crop water stress index. Wireless sensing systems for canopy temperature and soil water content, among other labile properties, will be discussed in view of their use in SSVRI systems.