Carbapenemase-producing Klebsiella pneumoniae (CPKP) emerged in Greece in 2002 and became endemic thereafter. Driven by a notable variability in the phenotypic testing results for carbapenemase production in K. pneumoniae isolates from the intensive care units (ICUs) of our hospital, we performed a study to assess the molecular epidemiology of CPKP isolated between 2016 and 2019 using pulse-field gel electrophoresis (PFGE) including isolates recovered from 165 single patients. We investigated the molecular relatedness among strains recovered from rectal surveillance cultures and from respective subsequent infections due to CPKP in the same individual (48/165 cases). For the optimal interpretation of our findings, we carried out a systematic review regarding the clonality of CPKP isolated from clinical samples in ICUs in Europe. In our study, we identified 128 distinguishable pulsotypes and 17 clusters that indicated extended dissemination of CPKP within the hospital ICU setting throughout the study period. Among the clinical isolates, 122 harbored KPC genes (74%), 2 harbored KPC+NDM (1.2%), 38 harbored NDM (23%), 1 harbored NDM+OXA-48 (0.6%), 1 harbored NDM+VIM (0.6%) and 1 harbored the VIM (0.6%) gene. Multiple CPKP strains in our hospital have achieved sustained transmission. The polyclonal endemicity of CPKP presents a further threat for the selection of pathogens resistant to last-resort antimicrobial agents.