Final answer:
The liver and kidneys are primarily responsible for the processing and excretion of drugs; the liver detoxifies substances while the kidneys filter and eliminate them via urine.
Step-by-step explanation:
The two organs most involved in the processing and excretion of drugs are the liver and the kidneys. The liver plays a critical role in detoxification, modifying toxic substances into less harmful products before they are eliminated. This transformation process is crucial and one function tested during liver function tests. Once detoxified by the liver, substances, including drugs, may become more water-soluble and hence easier for the kidneys to handle. The kidneys are responsible for filtering these converted substances, among others, out of the bloodstream. They facilitate removal through urine production, which involves processes like glomerular filtration, tubular secretion, and tubular reabsorption. Efficient kidney function is vital for maintaining homeostasis in the body by managing the balance of water and soluble substances like salts and minerals.