Many traits show plastic phenotypic variation across environments, captured by their norms of reaction. These reaction norms may be discrete or continuous, and can substantially vary in shape across organisms and traits, making it difficult to compare amounts and types of plasticity among (or even within) studies. In addition, the evolutionary potential of phenotypic traits and their plasticity in heterogeneous environments critically depends on how reaction norms vary genetically, but there is no consensus on how this should be quantified. Here, we propose a partitioning of phenotypic variance across genotypes and environments that jointly address these challenges. We start by distinguishing the components of phenotypic variance arising from the average reaction norm across genotypes, genetic variation in reaction norms (with additive and non-additive components), and a residual that cannot be predicted from the genotype and the environment. We then further partition the genetic variance of the trait (additive or not) into an environment-blind component and a component arising from genetic variance in plasticity. We show that the additive components can be expressed, and further decomposed according to the relative contributions from each parameter, using what we describe as the reaction norm gradient. This allows for a very general framework applicable from the character-state to curve-parameter approaches, including polynomial functions, or arbitrary non-linear models. To facilitate the use of this variance decomposition, we provide the Reacnorm R package, including a practical tutorial. Overall the toolbox we develop should serve as a basis for a unifying and deeper understanding of the variation and genetics of reaction norms and plasticity, as well as more robust comparative studies of plasticity across organisms and traits.