Step 1: Think of the inguinal ligament as a bridge stretched from the anterior superior iliac spine to the pubic tubercle, with a tunnel underneath through which contents move between abdomen and thigh.
Step 2: Lateral part of this tunnel is muscular and transmits psoas major and iliacus along with the femoral nerve. Medial part is vascular and transmits the femoral artery and femoral vein inside the femoral sheath, with the femoral canal most medially.
Step 3: Checking each option - the psoas major clearly runs behind the ligament into the thigh, the femoral vein passes behind it in the vascular compartment, and the femoral branch of the genitofemoral nerve also travels behind the ligament to reach the upper thigh skin.
Step 4: Because every listed structure passes behind the inguinal ligament, the answer is All.
\[\boxed{\text{All of them}}\]