RNA folding from sequences into secondary structures is a simple yet powerful, biophysically grounded model of a genotype-phenotype map in which concepts like plasticity, evolvability, epistasis, and modularity can not only be precisely defined and statistically measured but also reveal simultaneous and profoundly non-independent effects of natural selection. Molecular plasticity is viewed here as the capacity of an RNA sequence to assume a variety of energetically favorable shapes by equilibrating among them at constant temperature. Through simulations based on experimental designs, we study the dynamics of a population of RNA molecules that evolve toward a predefined target shape in a constant environment. Each shape in the plastic repertoire of a sequence contributes to the overall fitness of the sequence in proportion to the time the sequence spends in that shape. Plasticity is costly, since the more shapes a sequence can assume, the less time it spends in any one of them. Unsurprisingly, selection leads to a reduction of plasticity (environmental canalization). The most striking observation, however, is the simultaneous slow-down and eventual halting of the evolutionary process. The reduction of plasticity entails genetic canalization, that is, a dramatic loss of variability (and hence a loss of evolvability) to the point of lock-in. The causal bridge between environmental canalization and genetic canalization is provided by a correlation between the set of shapes in the plastic repertoire of a sequence and the set of dominant (minimum free energy) shapes in its genetic neighborhood. This statistical property of the RNA genotype-phenotype map, which we call plastogenetic congruence, traps populations in regions where most genetic variation is phenotypically neutral. We call this phenomenon neutral confinement. Analytical models of neutral confinement, made tractable by the assumption of perfect plastogenetic congruence, formally connect mutation rate, the topography of phenotype space, and evolvability. These models identify three mutational regimes: that corresponding to neutral confinement, an exploration threshold corresponding to a breakdown of neutral confinement with the simultaneous persistence of the dominant phenotype, and a classic error threshold corresponding to the loss of the dominant phenotype. In a final step, we analyze the structural properties of canalized phenotypes. The reduction of plasticity leads to extreme modularity, which we analyze from several perspectives: thermophysical (melting--the RNA version of a norm of reaction), kinetic (folding pathways--the RNA version of development), and genetic (transposability--the insensitivity to genetic context). The model thereby suggests a possible evolutionary origin of modularity as a side effect of environmental canalization.