In the first part, the following mechanisms involved in different forms of cell death are considered, with a view to identifying potential therapeutic targets: tumour necrosis factor receptors (TNFRs) and their engagement by tumour necrosis factor-alpha (TNF-α); poly [ADP-ribose] polymerase (PARP)-1 cleavage; the apoptosis signalling kinase (ASK)-c-Jun N-terminal kinase (JNK) axis; lysosomal permeability; activation of programmed necrotic cell death; oxidative stress, caspase-3 inhibition and parthanatos; activation of inflammasomes by reactive oxygen species and the development of pyroptosis; oxidative stress, calcium dyshomeostasis and iron in the development of lysosomal-mediated necrosis and lysosomal membrane permeability; and oxidative stress, lipid peroxidation, iron dyshomeostasis and ferroptosis. In the second part, there is a consideration of the role of lethal and sub-lethal activation of these pathways in the pathogenesis and pathophysiology of neurodegenerative and neuroprogressive disorders, with particular reference to the TNF-α-TNFR signalling axis; dysregulation of ASK-1-JNK signalling; prolonged or chronic PARP-1 activation; the role of pyroptosis and chronic inflammasome activation; and the roles of lysosomal permeabilisation, necroptosis and ferroptosis. Finally, it is suggested that, in addition to targeting oxidative stress and inflammatory processes generally, neuropsychiatric disorders may respond to therapeutic targeting of TNF-α, PARP-1, the Nod-like receptor NLRP3 inflammasome and the necrosomal molecular switch receptor-interacting protein kinase-3, since their widespread activation can drive and/or exacerbate peripheral inflammation and neuroinflammation even in the absence of cell death. To this end, the use is proposed of a combination of the tetracycline derivative minocycline and N-acetylcysteine as adjunctive treatment for a range of neuropsychiatric disorders.