Lysosomes contain hydrolase enzymes to digest substances taken into the cell by phagocytosis.
Neutrophils, macrophages, and other phagocytic cells have granules derived from lysosomes, which fuse with incoming vesicles to produce phagosomes
Peroxisomes have peroxidase enzymes used in detoxification.
Lysosomes and peroxisomes are often used for apoptosis, the self destruction of a cell due to its age, health, or other condition.