**Core Concept**
The posterior compartment of the thigh is a muscular region that includes the hamstrings and other deep muscles. Its blood supply is derived from the major arteries that run along the posterior aspect of the thigh, which is crucial for understanding potential vascular complications in this region.

**Why the Correct Answer is Right**
The blood supply to the posterior compartment of the thigh is primarily provided by the popliteal artery, which is a continuation of the femoral artery. The popliteal artery divides into two main branches: the anterior tibial artery and the tibial nerve. However, the main supply to the posterior compartment is through the short posterior branches of the popliteal artery, which anastomose with the inferior gluteal artery and the medial circumflex femoral artery. This rich network of vessels ensures adequate perfusion of the hamstrings and other deep muscles in the posterior compartment.

**Why Each Wrong Option is Incorrect**
**Option A:** This option is incorrect because it does not accurately represent the primary blood supply to the posterior compartment of the thigh. The femoral artery gives rise to the popliteal artery, which is the main supplier of blood to this region.

**Option B:** This option is incorrect because it mentions the inferior gluteal artery, which primarily supplies the gluteus maximus muscle and the overlying skin, rather than the posterior compartment of the thigh.

**Option C:** This option is incorrect because it mentions the medial circumflex femoral artery, which primarily supplies the femoral head and the neck of the femur, rather than the posterior compartment of the thigh.

**Clinical Pearl / High-Yield Fact**
The posterior compartment of the thigh is susceptible to compartment syndrome, which can occur due to increased pressure within the muscle compartments. This can be caused by trauma, exercise, or other factors that lead to swelling and decreased blood flow to the muscles. Prompt recognition and treatment of compartment syndrome are essential to prevent muscle damage and other complications.

**Correct Answer: D. Popliteal artery.**