The liver is the main organ where exogenous chemicals are taken up to be metabolised and eventually excreted in bile. As a consequence the liver is exposed to high concentrations of these chemicals and also there can be bioactivation producing toxic secondary chemicals. The liver suffers different types of injury, depending on the type of specialised liver cell and molecular pathways that are most affected by the offending chemical. 

These are the types of liver injury that occur with examples of the injurious chemicals:

Fatty liver or steatosis
(an increase in the lipid content of the liver to >5% by weight)
Ethanol, tamoxifen, valproic acid, amiodarone
Hepatocyte death
(via necrosis or apoptosis)
Ethanol, acetaminophen (= paracetamol)*, amanitins
Immune mediated response 
(activation of macrophages or neutrophils, or antibody induction)
Ethanol, halothane, diclofenac
Cholestasis (decrease in bile formation) Oestrogens, cyclosporin A, chlorpromazine
Bile duct damage Amoxicillin
Sinusoidal damage Anabolic steroids, pyrrolizidine alkaloids, cyclophosphamide
Fibrosis & cirrhosis Ethanol, vitamin A, iron
Tumours Aflatoxin, androgens, arsenic
* The most frequent cause of drug induced liver failure, due to accidental or intentional overdose

 

The susceptibility of the kidney to toxins is partly due to its physiologic and anatomic features; although the kindeys are only equivalent to 0.5% of body mass, they receive 20% or more of the cardiac output. As a consequence any circulating drug is delivered to the kidneys in relatively high amount. Also, the process of forming concentrated urine tends to concentrate toxins in the tubular fluid so that a non-toxic concentration of a chemical in plasma may reach toxic levels in the kidney. Some concentrated compounds may even precipitate out (crystallise) and cause tubular obstruction. 
Many toxins have their major effects on a specific region of the nephron, for example the proximal tubule is vulnerable to nephrotoxic antibiotics, the glomerulus is the primary site for immune complexes and the cells and structures of the papilla are the target of chronically consumed analgesics. The reasons for these site specific injuries are complex.

These are the types of kidney injury that occur with examples of the injurious chemicals:

Pre-renal (hypovolaemia) ACE inhibitors, diuretics, anti-hypertensives
Vasoconstriction NSAIDs, radiocontrast agents, Amphotericin B
Crystalluria Acyclovir, anti-HIV Protease inhibitors
Tubular toxicity Oestrogens, cyclosporin A, chlorpromazine
Endothelial damage Cocaine, quinine
Glomerulopathy NSAIDS
Interstitial inflammation NSAIDS, antibiotics, diuretics,