Since the establishment of the renormalization group theory, it has been known that systems of critical phenomena typically possess an upper critical dimension dc (dc=4 for the O(n) model), such that in spatial dimensions at or higher than the dc, the thermodynamic behavior is governed by critical exponents taking mean-field values. In contrast to the simplicity of the thermodynamic behavior, the theory of finite-size scaling (FSS) for the d>dc O(n) model was surprisingly subtle and had remained the subject of ongoing debate till recently, when a two-length scaling ansatz for the two-point correlation function was conjectured, numerically confirmed, and partly supported by analytical calculations.