The global crude oil market has gone through two important phases over the recent years. The first one was the price collapse that started in the third quarter of 2014 and continued until mid-2016. The second phase occurred in late 2016, after major producers within and outside OPEC agreed to cut production in order to adjust the ongoing fall in oil prices, which is now known as the OPEC+ agreement. This paper analyzes the effects of these recent developments on the market structure and on the behavior of major producers in the market. To this end, we develop a partial equilibrium model with a spatial structure for the global crude oil market and simulate the market for the period between 2013 and 2017 under oligopolistic, cartel and perfectly competitive market structure setups. The simulation results reveal that, although the oligopolistic market structures fit overall well to the realized market outcomes, they are not successful at explaining the low prices during 2015 and 2016, which instead are closer to estimated competitive levels. Moreover, we further suggest that from 2014 onward, the market power potential of major suppliers has shrunk considerably, supporting the view that the market has become more competitive. We also analyze the Saudi Arabia- and Russia-led OPEC+ agreement, and find that planned production cuts in 2017, particularly of Saudi Arabia (486 thousand barrels/day) and Russia (300 thousand barrels/day), were below the levels of estimated non-competitive market structure setups. This explains why the oil prices did not recover to pre-2014 levels although a temporary adjustment was observed in 2017.