We critically appraised the Diósi-Penrose collapse model, discussing diverse points that need to be clarified by further research. They include the width of the mass distribution, whose main proposal is at odds with non-interferometric experimental results; the selection of preferred basis, whose status is not as straightforward as in the decoherence program; the gravitational self-energy saturation, which leads to a nonintuitive result where the collapse time does not depend on the superposition displacement; and the extensivity problem, which seems to imply that macroscopic system may have too long collapse times.