The clinical impact of infections due to extended-spectrum β-lactamase (ESBL)- and/or carbapenemase-producing Enterobacterales (Ent) has reached dramatic levels worldwide. Infections due to these multidrug-resistant (MDR) pathogens—especially Escherichia coli and Klebsiella pneumoniae—may originate from a prior asymptomatic intestinal colonization that could also favor transmission to other subjects. It is therefore desirable that gut carriers are rapidly identified to try preventing both the occurrence of serious endogenous infections and potential transmission. Together with the infection prevention and control countermeasures, any strategy capable of effectively eradicating the MDR-Ent from the intestinal tract would be desirable. In this narrative review, we present a summary of the different aspects linked to the intestinal colonization due to MDR-Ent. In particular, culture- and molecular-based screening techniques to identify carriers, data on prevalence and risk factors in different populations, clinical impact, length of colonization, and contribution to transmission in various settings will be overviewed. We will also discuss the standard strategies (selective digestive decontamination, fecal microbiota transplant) and those still in development (bacteriophages, probiotics, microcins, and CRISPR-Cas-based) that might be used to decolonize MDR-Ent carriers.