Macrophages are professional phagocytes, responsible for clearing apoptotic cells and debris, and preventing the buildup of necrotic tissue. Factors secreted by these cells, including cytokines and reactive oxygen species can, however, cause significant tissue damage leading to an escalating inflammatory condition. We report on progress in mathematical modeling of two diseases in which these innate immune system cells may be adversely implicated, Alzheimer’s Disease (AD) and Type 1 diabetes (T1D). We discuss the dual roles of microglia in the brain and macrophages in the pancreas. In T1D, macrophage activity following some initial stimulus could set the stage for insulitis and eventual destruction of insulin-secreting beta-cells by cytotoxic T cells. In AD, the reaction of microglia to amyloid beta can escalate to neuroinflammation and lead to stress and death of neurons. A fine balance exists between factors that ensure resolution of inflammation versus those that accelerate it. Mathematical modeling can help to rigorously and quantitatively explore how these competing influences play out. A comparison of the feedbacks and conditions for healthy or pathological outcomes in the two diseases is discussed. In the case of T1D, theoretical work has been accompanied by in vitro experiments to quantify macrophage phagocytosis, including rates of engulfment and digestion of apoptotic cells. These experiments reveal significant differences between animals prone to T1D, the non-obese diabetic (NOD) mice versus normal (Balb/c) mice. We found that NOD mouse macrophages engulf apoptotic cells more slowly than their normal counterparts. We have conjectured that this defect may be significant in initial stages of T1D pathogenesis, and we continue to explore this hypothesis. Mathematical models have led to improved experimental design, and have been informed by experimental results.