ABSTRACT In this work, we study the formation and chemical evolution of the Galactic bulge with particular focus on the abundance pattern ([Mg/Fe] versus [Fe/H]), metallicity, and age distribution functions. We consider detailed chemical evolution models for the Galactic bulge and inner disc, with the aim of shedding light on the connection between these components and the origin of bulge stars. In particular, we first present a model assuming a fast and intense star formation, with the majority of bulge stars forming on a time-scale less than 1 Gyr. Then we analyse the possibility of two distinct stellar populations in the bulge, as suggested by Gaia-ESO and APOGEE data. These two populations, one metal poor and the other metal rich, can have had two different origins: (i) the metal rich formed after a stop of ∼250 Myr in the star formation rate of the bulge or (ii) the metal-rich population is made of stars formed in the inner disc and brought into the bulge by the early secular evolution of the bar. We also examine the case of multiple starbursts in the bulge with consequent formation of multiple populations, as suggested by studies of microlensed stars. After comparing model results and observations, we suggest that the most likely scenario is that there are two main stellar populations, both made mainly by old stars (>10 Gyr), with the metal-rich and younger one formed from inner thin disc stars, in agreement with kinematical arguments. However, on the basis of dynamical simulations, we cannot completely exclude that the second population formed after a stop in the star formation during the bulge evolution, so that all the stars formed in situ.