Collapse theories stand in opposition to many-world theories, in that they hold that a process of wavefunction collapse curtails the branching of the wavefunction and removes unobserved behaviour. Objective collapse theories differ from the Copenhagen interpretation in regarding both the wavefunction and the process of collapse as ontologically objective. The Copenhagen interpretation includes collapse, but it is non-committal about the objective reality of the wave function, and because of that it is possible to regard Copenhagen-style collapse as a subjective or informational phenomenon. In objective theories, there is an ontologically real wave of some sort corresponding to the mathematical wave function, and collapse occurs randomly ("spontaneous localization"), or when some physical threshold is reached, with observers having no special role.
Objective collapse theories regard the present formalism of quantum mechanics as incomplete, in some sense. (For that reason it is more correct to call them theories than interpretations.) They divide into two subtypes, depending on how the hypothesised mechanism of collapse stands in relation to the unitary evolution of the wavefunction.
The fact that these theories seek to extend the formalism is considered as violation of the principle of parsimony by some.
GRW collapse theories have unique problems. In order to keep these theories from violating the principle of the conservation of energy, the mathematics requires that any collapse be incomplete. Almost all of the wave function is contained at the one measurable (and measured) value, but there are one or more small "tails" where the function should intuitively equal zero but mathematically does not. It is not clear how to interpret these "tails." They might mean that a small bit of matter has collapsed elsewhere than the measurement indictes, that with very low probability an object might "jump" from one collapsed state to another, or something else entirely. All of these options seem counterintuitive.
Additionally, Peter Lewis argues that due to GRW's relaxing of the requirement that mutually exclusive states of affairs must be represented by orthogonal vectors (the standard orthonormal rule, or SOR) arithmetic will fail to apply to ordinary macroscopic objects.