Pulmonary hypertension (PH) is a severe and chronic disease characterized by increased pulmonary vascular resistance and remodeling, often precipitating right-sided heart dysfunction and death. Although the condition is progressive and incurable, current therapies for the disease focus on multiple different drugs and general supportive therapies to manage symptoms and prolong survival, ranging from medications more specific to pulmonary arterial hypertension (PAH) to exercise training. Moreover, there are multiple studies exploring novel experimental drugs and therapies including unique neurostimulation, to help better manage the disease. Here, we provide a narrative review focusing on current PH treatments that target multiple underlying biochemical mechanisms, including imbalances in vasoconstrictor–vasodilator and autonomic nervous system function, inflammation, and bone morphogenic protein (BMP) signaling. We also focus on the potential of novel therapies for managing PH, focusing on multiple types of neurostimulation including acupuncture. Lastly, we also touch upon the disease’s different subgroups, clinical presentations and prognosis, diagnostics, demographics, and cost.