Adequate pain management, particularly chronic pain, remains a major challenge associated with modern-day medicine. Current pharmacotherapy offers unsatisfactory long-term solutions due to serious side effects related to the chronic administration of analgesic drugs. Morphine and structurally related derivatives (e.g., oxycodone, oxymorphone, buprenorphine) are highly effective opioid analgesics, mediating their effects via the activation of opioid receptors, with the mu-opioid receptor subtype as the primary molecular target. However, they also cause addiction and overdose deaths, which has led to a global opioid crisis in the last decades. Therefore, research efforts are needed to overcome the limitations of present pain therapies with the aim to improve treatment efficacy and to reduce complications. This review presents recent chemical and pharmacological advances on 14-oxygenated-N-methylmorphinan-6-ones, in the search of safer pain therapeutics. We focus on drug design strategies and structure–activity relationships on specific modifications in positions 5, 6, 14 and 17 on the morphinan skeleton, with the goal of aiding the discovery of opioid analgesics with more favorable pharmacological properties, potent analgesia and fewer undesirable effects. Targeted molecular modifications on the morphinan scaffold can afford novel opioids as bi- or multifunctional ligands targeting multiple opioid receptors, as attractive alternatives to mu-opioid receptor selective analgesics.