Hidradenitis suppurativa (HS) is an inflammatory skin disease that causes painful lesions in the axilla (underarm), inguinal (groin) and anogenital (anal/genital) regions. This study will assess how safe and effective upadacitinib is in treating adult and adolescent participants with moderate to severe HS who have failed to respond to or are intolerant of anti-tumor necrosis factor (TNF) therapy. Adverse events and change in disease activity will be assessed. Upadacitinib is an approved drug for ulcerative colitis, atopic dermatitis, rheumatoid arthritis, psoriatic arthritis, and axial spondylarthritis and is being developed for the treatment of HS. This study is double-blinded, meaning that neither the trial participants nor the study doctors will know who will be given upadacitinib and who will be given placebo. This study is comprised of 3 periods. In Period 1, participants are randomized into 2 groups called treatment arms where each group receives a different treatment. There is a 1 in 2 chance that participants will be assigned to placebo. In Period 2, participants are placed into 6 different groups depending on their placement and results in Period 1. Period 3 is the long-term extension period where participants will continue treatment from Period 2. Approximately 1328 adult and adolescent participants diagnosed with HS will be enrolled in approximately 300 sites worldwide. Participants will receive oral tablets of upadacitinib or placebo once daily for 36 weeks in Period 1 and Period 2. Eligible participants from Period 1 and Period 2 will enter Period 3 and receive oral tablets of upadacitinib or placebo once daily for 68 weeks. Participants will be followed up for approximately 30 days. There may be higher treatment burden for participants in this trial compared to their standard of care. Participants will attend regular outpatient visits during the study. The effect of the treatment will be checked by medical assessments, checking for side effects and completing questionnaires.