Alien plant species have been essential for farming and agro-forestry systems and for their supply of food, fiber, tannins, resins or wood from antiquity to the present. They also contributed to supporting functions and regulating services (water, soil, biodiversity) and to the design of landscapes with high cultural and scenic value. Some of those species were intentionally introduced, others arrived accidentally, and a small proportion escaped, naturalized and became invasive in natural ecosystems—these are known as invasive alien species (IAS). Here, invasive means that these species have some significant negative impact, either by spreading from human-controlled environments (e.g. fields, gardens) to natural ecosystems, where they can cause problems to native species, or to other production systems or urban areas, impacting on agricultural, forestry activities or human health. Socio-environmental impacts associated with plant invasions have been increasingly recognized worldwide and are expected to increase considerably under changing climate or land use. Early detection tools are key to anticipate IAS and to prevent and control their impacts. In this chapter, we focus on crop and non-crop alien plant species for which there is evidence or prediction of invasive behaviour and impacts. We provide insights on their history, patterns, risks, early detection, forecasting and management under climate change. Specifically, we start by providing a general overview on the history of alien plant species in agricultural and agroforestry systems worldwide (Sect. 1). Then, we assess patterns, risks and impacts resulting from alien plants originally cultivated and that became invasive outside cultivation areas (Sect. 2). Afterwards, we provide several considerations for managing the spread of invasive plant species in the landscape (Sect. 3). Finally, we discuss challenges of alien plant invasions for agricultural and agroforest systems, in the light of climate change (Sect. 4).