Pain is an unpleasant sensory and emotional experience that affects every aspect of a patient’s life and which may be treated through different pharmacological and non-pharmacological approaches. Analgesics are the drugs most commonly used to treat pain, and in specific situations, the use of opioids may be considered with caution. These drugs, in fact, do not always induce optimal analgesia in patients, and several problems are associated with their use. The purpose of this narrative review is to describe the pharmacological approaches currently used for the management of chronic pain. We review several aspects, from the pain-scale-based methods currently available to assess the type and intensity of pain, to the most frequently administered drugs (non-narcotic analgesics and narcotic analgesics), whose pharmacological characteristics are briefly reported. Overall, we attempt to provide an overview of different pharmacological treatments while also illustrating the relevant guidelines and indications. We then report the strategies that may be used to reduce problems related to opioid use. Specifically, we focus our attention on therapeutic drug monitoring (TDM), a tool that could help clinicians select the most suitable drug and dose to be used for each patient. The actual potential of using TDM to optimize and personalize opioid-based pain treatments is finally discussed based on recent scientific reports.