The assembly of the Milky Way bulge is an old topic in astronomy, one now in a period of renewed and rapid development. That is due to tremendous advances in observations of bulge stars, motivating observations of both local and high-redshift galaxies, and increasingly sophisticated simulations. The dominant scenario for bulge formation is that of the Milky Way as a nearly pure disk galaxy, with the inner disk having formed a bar and buckled. This can potentially explain virtually all bulge stars with [Fe/H] ≳ −1.0, which comprise 95% of the stellar population. The evidence is the incredible success in N-body models of this type in making non-trivial, non-generic predictions, such as the rotation curve and velocity dispersion measured from radial velocities, and the spatial morphologies of the peanut/X-shape and the long bar. The classical bulge scenario, whereby the bulge formed from early dissipative collapse and mergers, remains viable for stars with [Fe/H] ≲ −1.0 and potentially a minority of the other stars. A classical bulge is expected from Λ-CDM cosmological simulations, can accentuate the properties of an existing bar in a hybrid system, and is most consistent with the bulge abundance trends such as [Mg/Fe], which are elevated relative to both the thin and thick disks. Finally, the clumpy-galaxy scenario is considered, as it is the correct description of most Milky Way precursors given observations of high-redshift galaxies. Simulations predict that these star-forming clumps will sometimes migrate to the centres of galaxies where they may form a bulge, and galaxies often include a bulge clump as well. They will possibly form a bar with properties consistent with those of the Milky Way, such as the exponential profile and metallicity gradient. Given the relative successes of these scenarios, the Milky Way bulge is plausibly of composite origin, with a classical bulge and/or inner halo numerically dominant for stars with [Fe/H] ≲ −1.0, a buckling thick disk for stars with − 1.0 ≲ [Fe/H]] ≲ -0.50 perhaps descended from the clumpy-galaxy phase, and a buckling thin disk for stars with [Fe/H] ≳ −0.50. Overlaps from these scenarios are uncertain throughout.