The present invention pertains generally to the field of therapeutic compounds. More specifically the present invention pertains to certain substituted N-(4-hydroxy-4-methyl-cyclohexyl)-4-phenyl-benzenesulfonamide and N-(4-hydroxy-4-methyl -cyclohexyl)-4-(2-pyridyl)benzenesulfonamide compounds (collectively referred to herein as HMC compounds) that are useful, for example, in the treatment of disorders (e.g., diseases) including, inflammation and/or joint destruction and/or bone loss; disorders mediated by excessive and/or inappropriate and/or prolonged activation of the immune system; inflammatory and autoimmune disorders, for example, rheumatoid arthritis; psoriasis; psoriatic arthritis; chronic obstructive pulmonary disease (COPD); asthma; atherosclerosis; inflammatory bowel disease; ankylosing spondylitis; multiple sclerosis; systemic lupus erythematosus; Sjogren's syndrome; a disorder associated with bone loss, such as bone loss associated with excessive osteoclast activity in rheumatoid arthritis, osteoporosis, cancer-associated bone disease, or Paget's disease; cancer, such as a haematological malignancy, such as multiple myeloma, leukemia, or lymphoma, or a solid tumour cancer, such as bladder cancer, breast cancer (female and/or male), colon cancer, renal cell carcinoma, kidney cancer, lung cancer, pancreatic cancer, gastric cancer, prostate cancer, brain cancer, skin cancer, thyroid cancer, basal cell ameloblastoma, or melanoma; a disorder associated with fibrosis, such as systemic sclerosis or scleroderma; or a rare vasculitide, such as Behçet's disease. The present invention also pertains to pharmaceutical compositions comprising such compounds, and the use of such compounds and compositions, for example, in therapy.