MicroRNAs (miRNAs) and long non-coding RNAs (lncRNAs) are components of many signaling pathways associated with tumor aggressiveness and cancer metastasis. Some lncRNAs are classified as competitive endogenous RNAs (ceRNAs) that bind to specific miRNAs to prevent interaction with target mRNAs. Studies have shown that the hepatocyte growth factor/mesenchymal-epithelial transition factor (HGF/c-Met) pathway is involved in physiological and pathological processes such as cell growth, angiogenesis, and embryogenesis. Overexpression of c-Met can lead to sustained activation of downstream signals, resulting in carcinogenesis, metastasis, and resistance to targeted therapies. In this review, we evaluated the effects of anti-oncogenic and oncogenic non-coding RNAs (ncRNAs) on c-Met, and the interactions among lncRNAs, miRNAs, and c-Met in cancer using clinical and tissue chromatin immunoprecipition (ChIP) analysis data. We summarized current knowledge of the mechanisms and effects of the lncRNAs/miR-34a/c-Met axis in various tumor types, and evaluated the potential therapeutic value of lncRNAs and/or miRNAs targeted to c-Met on drug-resistance. Furthermore, we discussed the functions of lncRNAs and miRNAs in c-Met-related carcinogenesis and potential therapeutic strategies.