The unsatisfactory response of colorectal cancer (CRC) to pharmacological treatment contributes to the substantial global health burden caused by this disease. Over the last few decades, CRC has become the cause of more than 800,000 deaths per year. The reason is a combination of two factors: (i) the late cancer detection, which is being partially solved by the implementation of mass screening of adults over age 50, permitting earlier diagnosis and treatment; (ii) the inadequate response of advanced unresectable tumors (i.e., stages III and IV) to pharmacological therapy. The latter is due to the existence of complex mechanisms of chemoresistance (MOCs) that interact and synergize with each other, rendering CRC cells strongly refractory to the available pharmacological regimens based on conventional chemotherapy, such as pyrimidine analogs (5-fluorouracil, capecitabine, trifluridine, and tipiracil), oxaliplatin, and irinotecan, as well as drugs targeted toward tyrosine kinase receptors (regorafenib, aflibercept, bevacizumab, cetuximab, panitumumab, and ramucirumab), and, more recently, immune checkpoint inhibitors (nivolumab, ipilimumab, and pembrolizumab). In the present review, we have inventoried the genes involved in the lack of CRC response to pharmacological treatment, classifying them into seven groups (from MOC-1 to MOC-7) according to functional criteria to identify cancer cell weaknesses. This classification will be useful to pave the way for developing sensitizing tools consisting of (i) new agents to be co-administered with the active drug; (ii) pharmacological approaches, such as drug encapsulation (e.g., into labeled liposomes or exosomes); (iii) gene therapy interventions aimed at restoring the impaired function of some proteins (e.g., uptake transporters and tumor suppressors) or abolishing that of others (such as export pumps and oncogenes).