fine structure
Look at a hydrogen spectral line with a good spectrometer and the single line you expected from the Bohr model turns out to be a close-spaced cluster. That splitting is the fine structure: a set of small corrections to the simple energy levels, all traceable to the fact that the electron is a relativistic, spinning particle rather than a slow classical point.
Fine structure gathers three corrections, each of order alpha^2 relative to the gross Bohr energies (alpha ≈ 1/137 is the fine-structure constant, which is why the effect is 'fine'). They are: the relativistic kinetic-energy correction, -p^4/(8 m^3 c^2), from expanding the relativistic energy; the spin-orbit coupling; and the Darwin term, a contact interaction affecting only l = 0 states. Added together in hydrogen they produce a remarkably simple result — the corrected energy depends only on n and the total angular momentum j, not on l separately: E_(n,j) = -(13.6 eV/n^2)[1 + (alpha^2/n^2)(n/(j + 1/2) - 3/4)]. The same expression drops out exactly, to this order, from the Dirac equation.
Fine structure is where the hydrogen atom stops being a toy and becomes a precision laboratory; it is the reason spectral lines carry j-labels and the backdrop against which hyperfine structure and the Lamb shift are measured. The honest caveat is the l-degeneracy: at this order, levels with the same n and j but different l (for example 2S_(1/2) and 2P_(1/2)) come out exactly equal. That coincidence is an artifact of the Dirac-equation treatment; the tiny splitting between them, the Lamb shift, is a quantum-electrodynamic effect that lies outside fine structure altogether.
The hydrogen H-alpha line (n = 3 to n = 2, 656 nm) is not a single line: fine structure splits it into a handful of components spread over about 0.014 nm, corresponding to the different j-levels of the n = 2 and n = 3 shells. The overall fractional scale is alpha^2 ~ 5x10^-5.
Fine structure turns each Bohr line into a multiplet at the alpha^2 level.
Do not read the n,j-only dependence as saying l is irrelevant — l still labels the state and controls selection rules; it simply drops out of the energy at this order, and even that degeneracy is broken by the Lamb shift.