Anaplastic lymphoma kinase (ALK) translocation is a rare genetic disorder that underlies lung cancer development. The right choice of treatment policy in patients with ALK-positive non-small cell lung cancer can significantly improve survival rates. As a rule, these are young people, in whom the diagnosis is made at a late stage of the disease, when there are distant metastases; the liver and brain are often affected. And molecularly targeted therapy with ALK inhibitors is effective even in these cases. Crizotinib is the first ALK inhibitor that has been proven its antitumor activity. Resistance to crizotinib generally develops after 1—2 years of its use. In this case, the prescription of the second-generation drugs alectinib and ceritinib allows half of the patients to achieve a long objective response. The maximum antitumor effect is reached after the use of new ALK inhibitors as the first line. Today, alectinib demonstrates the best results: the median progression-free survival is more than 34 months. The drug has been shown a high activity in patients with brain metastases. This opens up new perspectives in the treatment of ALK-positive patients.