Amyotrophic lateral sclerosis (ALS) is a fatal neurodegenerative disorder characterized by the loss of motor neurons in the brain and spinal cord. While the exact causes of ALS are still unclear, the discovery that familial cases of ALS are related to mutations in the Cu/Zn superoxide dismutase (SOD1), a key antioxidant enzyme protecting cells from the deleterious effects of superoxide radicals, suggested that alterations in SOD1 functionality and/or aberrant SOD1 aggregation strongly contribute to ALS pathogenesis. A new scenario was opened in which, thanks to the generation of SOD1 related models, different mechanisms crucial for ALS progression were identified. These include excitotoxicity, oxidative stress, mitochondrial dysfunctions, and non-cell autonomous toxicity, also implicating altered Ca2+ metabolism. While most of the literature considers motor neurons as primary target of SOD1-mediated effects, here we mainly discuss the effects of SOD1 mutations in non-neuronal cells, such as glial and skeletal muscle cells, in ALS. Attention is given to the altered redox balance and Ca2+ homeostasis, two processes that are strictly related with each other. We also provide original data obtained in primary myocytes derived from hSOD1(G93A) transgenic mice, showing perturbed expression of Ca2+ transporters that may be responsible for altered mitochondrial Ca2+ fluxes. ALS-related SOD1 mutants are also responsible for early alterations of fundamental biological processes in skeletal myocytes that may impinge on skeletal muscle functions and the cross-talk between muscle cells and motor neurons during disease progression.