This volume elaborates the idea that harmonic analysis on a spherical variety X is intimately connected to the Langlands program. In the local setting, the key conjecture is that the spectral decomposition of L²(X) is controlled by a dual group attached to X . Guided by this, the authors develop a Plancherel formula for L²(X) , formulated in terms of simpler spherical varieties which model the geometry of X at infinity. This local study is then related to global conjectures - namely, conjectures about period integrals of automorphic forms over spherical subgroups.