The immunomodulatory imide drug (IMiD) class, which includes the founding drug member thalidomide and later generation drugs, lenalidomide and pomalidomide, has dramatically improved the clinical treatment of specific cancers, such as multiple myeloma, and it combines potent anticancer and anti-inflammatory actions. These actions, in large part, are mediated by IMiD binding to the human protein cereblon that forms a critical component of the E3 ubiquitin ligase complex. This complex ubiquitinates and thereby regulates the levels of multiple endogenous proteins. However, IMiD-cereblon binding modifies cereblon’s normal targeted protein degradation towards a new set of neosubstrates that underlies the favorable pharmacological action of classical IMiDs, but also their adverse actions—in particular, their teratogenicity. The ability of classical IMiDs to reduce the synthesis of key proinflammatory cytokines, especially TNF-α levels, makes them potentially valuable to reposition as drugs to mitigate inflammatory-associated conditions and, particularly, neurological disorders driven by an excessive neuroinflammatory element, as occurs in traumatic brain injury, Alzheimer’s and Parkinson’s diseases, and ischemic stroke. The teratogenic and anticancer actions of classical IMiDs are substantial liabilities for effective drugs in these disorders and can theoretically be dialed out of the drug class. We review a select series of novel IMiDs designed to avoid binding with human cereblon and/or evade degradation of downstream neosubstrates considered to underpin the adverse actions of thalidomide-like drugs. These novel non-classical IMiDs hold potential as new medications for erythema nodosum leprosum (ENL), a painful inflammatory skin condition associated with Hansen’s disease for which thalidomide remains widely used, and, in particular, as a new treatment strategy for neurodegenerative disorders in which neuroinflammation is a key component.