Apoptosis is a form of physiological cell death that typically initiates from isolated points and spreads to all nooks and crannies of the cytoplasm. The spread of apoptotic signals is important for spatially coordinating apoptosis, yet its mechanism remains unclear. Using quantitative live imaging of frog eggs, oocytes and cell-free egg extracts, we show that rather than by simple diffusion which slows down and peters out over longer distances, apoptotic signals are propagated by self-regenerating chemical waves (trigger waves) with a constant speed and sustained intensity. We show that trigger waves arise from positive feedback regulation, and propose that they may be a general mechanism for effective transmission of biological signals over long distances. While imaging egg extracts, we unexpectedly discovered that homogenized cytoplasm spontaneously re-organizes into compartments that resemble cells. Formation of these compartments requires microtubule, its associated motor protein dynein, and adenosine triphosphate (ATP), but not F-actin or centrosome. These compartments can undergo many consecutive cycles of mitotic divisions, cleaving like cells in an embryo. These findings show that the cytoplasm suffices to generate the basic spatial organization of the cell and retains prominent cellular functions.