Complex Regional Pain Syndrome (CRPS) after knee and hip arthroplasty is a rare but clinically significant condition characterized by disproportionate pain, vasomotor/sudomotor disturbances, and motor–trophic changes. This narrative review, with a focus on arthroplasty patients, summarizes the latest evidence on definition and classification (Budapest criteria and Valencia adaptation), epidemiology and risk factors, the place of CRPS within the “painful prosthesis” algorithm, and conservative, pharmacological, and advanced treatment options. Prospective data indicate that strict application of the Budapest criteria reduces overdiagnosis and confirms that CRPS is uncommon after total knee arthroplasty, although higher preoperative pain intensity and extent may increase risk. In hip arthroplasty, the evidence is limited mainly to case reports and small case series. Within diagnostic work-up, stepwise exclusion of prosthetic joint infection, mechanical assessment with radiography/CT, and targeted use of SPECT/CT (particularly in the knee) are essential before considering CRPS, while nuclear imaging is not specific for “confirming” CRPS. From a therapeutic standpoint, the cornerstone of effective management is early, multidisciplinary rehabilitation combined with multimodal analgesia. Randomized trials provide strong evidence for bisphosphonates, moderate benefit for short-course corticosteroids in the early inflammatory phase, limited adjunctive effects for gabapentinoids, and inconsistent findings regarding vitamin C. In refractory cases, sympathetic blocks, subanesthetic ketamine infusions (short-term effect), and neuromodulation—especially dorsal root ganglion stimulation for focal limb pain—may be useful. The review concludes by proposing a stepwise care pathway and highlighting research priorities, particularly the need for standardized outcome measures.