Classic Hodgkin lymphoma (cHL) is characterized by a few tumor cells surrounded by a protective, immunosuppressive tumor microenvironment composed of normal cells that are an active part of the disease. Hodgkin and Reed-Sternberg (HRS) cells evade the immune system through a variety of different mechanisms. They are invisible to antitumor effector T cells and natural killer cells and promote T cell exhaustion. Using cytokines and extracellular vesicles, they recruit normal cells, induce their proliferation, and “educate” (i.e., reprogram) them to become immunosuppressive and protumorigenic. Therefore, alternative treatment strategies, targeting not only tumor cells but also the tumor microenvironment, are being developed. Here we summarize current knowledge on the ability of HRS cells to build their microenvironment and to educate normal cells to become protective or immunosuppressive. We also describe therapeutic strategies to counteract formation of the tumor microenvironment and related processes leading to T cell exhaustion and repolarization of immunosuppressive tumor-associated macrophages.