Multidrug-resistant (MDR) Gram-negative bacteria cause a serious health risk worldwide. The increasing frequency of carbapenemase-producing organisms (CPOs) is especially concerning, due to the rapid dissemination of their transmissible genetic components containing carbapenemase genes, the lack of treatment alternatives for CPO-related infections, and the significant mortality incidences associated with these infections. Determining what an organism produces carbapenemase and, whether so, the particular carbapenemase order(s) associated with the degree of action that various substances show with particular carbapenemases varies. Additionally, CPOs are highly likely to spread amongst patients than non-CPOs carbapenem-resistant organisms, therefore more controlling prevention strategies are needed than they would be with non-CPOs. Humans and pets interact often, which facilitates the spread of Enterobacteriaceae that produce carbapenemases including Klebsiella pneumoniae, Klebsiella oxytoca, Escherichia coli, Enterobacter cloacae, Enterobacter xiangfangensis, and Salmonella enterica serovar Typhimurium. Also, carbapenems producing Pseudomonas aeruginosa and Acinetobacter baumannii were reported in companion animals. Current clinical practice relies on three main phenotypic assays to detect CPOs: (i) growth-based assays that measure carbapenem resistance based on organism growth in the presence of a carbapenem antibiotic (e.g., modified Hodge test and modified carbapenem inactivation method), (ii) hydrolysis methods that detect carbapenem degradation products [e.g., Carba NP test and matrix-assisted laser desorption–ionization time-of-flight mass spectrometry (MALDI-TOF MS)], and (iii) lateral flow immunoassays (LFIAs) that detect carbapenemase enzymes using specific antibodies. Even though no single test fits all the requirements for the most appropriate measure, as outlined in this review, there are numerous alternatives that are practical, accurate, affordable, and easy to use in clinical microbiology labs.