Human immunodeficiency virus (HIV) causes one of the most dangerous diseases—acquired immunodeficiency syndrome (AIDS). An estimated about 40 million people are currently living with HIV worldwide, most of whom are already on antiretroviral therapy. This makes the development of effective drugs to combat this virus very relevant. Currently, one of the dynamically developing areas of organic and medicinal chemistry is the synthesis and identification of new compounds capable of inhibiting HIV-1 integrase—one of the HIV enzymes. A significant number of studies on this topic are published annually. Many compounds inhibiting integrase incorporate pyridine core. Therefore, this review is an analysis of the literature on the methods for the synthesis of pyridine-containing HIV-1 integrase inhibitors since 2003 to the present.