Stem cells are an important component of tissue architecture. Identifying the exact regulatory circuits that can stably maintain tissue homeostasis is critical for our basic understanding of multicellular organisms. It is equally critical for figuring out how tumors circumvent this regulation, thus providing targets for treatment. Despite great strides in the understanding of the molecular components of stem-cell regulation, the overall mechanisms orchestrating tissue homeostasis are still far from being understood. Typically, tissue contains the stem cells and classes of more differentiated cells, including terminally differentiated cells. Each of these cell types can potentially secrete regulatory factors and/or respond to factors secreted by other types. The feedback can be positive or negative in nature. This gives rise to a bewildering array of possible mechanisms that drive tissue regulation. In this talk I describe a stochastic method of studying stem cell lineage regulation, which is based on population dynamics and ecological approaches. The method allows identification of possible numbers, types, and directions of control loops that are compatible with stability, keep the variance low, and possess a certain degree of robustness. I will then turn to the case study of the hematopoietic stem cell lineage and describe a mathematical model that has been fully calibrated based on recently measured murine parameters. I will show how the very architecture of the lineage gives rise to mutant invasion barriers, and how those can be overcome by pre-malignant cells aided by aging and inflammation.