Pulmonary hypertension (PH) is a hemodynamic and pathophysiologic state that can be found in multiple conditions with associated symptoms of dyspnea, decreased exercise tolerance, and progression to right heart failure. The World Health Organization has classified PH into five groups. The first group is pulmonary arterial hypertension (PAH), which can be idiopathic, heritable, due to drugs and toxins, or associated with conditions such as connective tissue diseases, congenital heart disease, portal hypertension, and others. The development of PAH is believed to result from smooth muscle cells and endothelial dysfunction that impairs production of vasodilators, including nitric oxide and prostacyclin. The importance of distinguishing this group from the other groups of PH is that there are PAH-specific drugs that target the molecular pathways that are pathogenic in the vascular derangements, leading to arterial hypertension, which should not be used in the other forms of PH. Other groups of PH include PH due to left heart disease, lung disease, chronic thromboembolic disease, as well as a miscellaneous category. Echocardiography is used to screen for PH and has varying sensitivity and specificity in detecting PH. Additionally, the right heart pressures estimated during echocardiogram often differ from those obtained during confirmatory testing with right heart catheterization. The most challenging PH diagnosis is in a case that does not fit one group of PH, but meets criteria that overlap between several groups. This also makes the treatment challenging because each group of PH is managed differently. This review provides an overview of the five groups of PH and discusses the diagnostic and therapeutic challenges of each.