Contemporary climate change is having widespread impacts on plant populations. Understanding how plants respond to this change is essential to our efforts to conserve them. The key climate responses of plant populations can be categorised into one of three types: migration, in situ adaptation, or extirpation. If populations are to avoid extirpation then migration and/or in situ adaptation is essential. In this review we first articulate the current and future constraints of plant populations, but trees in particular, to the different adaptation strategies (e.g. space availability, rate of change, habitat fragmentation, niche availability). Secondly, we assess the use of the most appropriate methods (e.g. natural environmental gradients, genome and transcriptome scans) for assessing and understanding adaptive responses and the capacity to adapt to future challenges. Thirdly, we discuss the best conservation approaches (e.g. assisted migration, biodiversity corridors, ex situ strategies) to help overcome adaptive constraints in plants. Our synthesis of plant, and particularly tree, responses and constraints to climate change adaptation, combined with the identification of conservation strategies designed to overcome constraints, will help deliver effective management actions to assist adaptation in the face of current and future climate change.