My honours project recently got published. I recommend reading the paper , but if that is too technical you can read my summary of it here. A reasonable question you might have is why we focussed on the liver and not muscle, because after all, isn’t muscle supposed to be the main organ involved in glucose control?
The contribution of muscle to whole body glucose uptake is often over-exaggerated. People bring up the fact that muscle is responsible for ~70-80% of insulin stimulated glucose uptake and use this to claim that muscle is responsible for ~70-80% of glucose uptake in the postprandial state (following a meal or an oral glucose tolerance test (OGTT))
The ~70-80% figure is correct, but the problem is that is that it comes from studies using a technique called the ‘euglycemic-hyperinsulinemic clamp’. The euglycemic-hyperinsulinemic clamp is the gold standard to measure insulin resistance** and involves infusing glucose and insulin into the blood to maintain euglycemia (normal glucose levels ¬5 mmol/l) and hyperinsulinemia (high insulin levels), often higher than what occur following an oral glucose tolerance test (see below  )
This method clearly doesn’t accurately represent what happens following a meal or OGTT, where muscle is responsible for ~30% of glucose uptake* . The conditions of the clamp favour muscle glucose uptake over other key organs such as the liver for a few of reasons:
· The main glucose transporter in muscle (GLUT4) has a higher affinity for glucose than the main glucose transport in the liver (GLUT2)  and the muscle version of hexokinase (the enzyme catalysing the first step of glycolysis) has a higher affinity for glucose than liver glucokinase . These differences mean muscle takes up more glucose during euglycemic conditions than the liver 
· When you eat a meal or do an OGTT the liver has the benefit of glucose and insulin levels being ¬2-3x higher in the portal vein compared to systemic circulation. This enhances liver glucose uptake and proportionally decreases glucose uptake by other tissues [4, 7, 8], but doesn’t occur when glucose and insulin are infused directly into the bloodstream
So it’s somewhat correct to say that muscle is responsible for ~70-80% of insulin stimulated glucose uptake, but this shouldn’t be extrapolated to what happens following a meal or OGTT where both insulin and glucose transiently increase
* In the fasted state the brain takes up most of the glucose and muscle is responsible for ~18% of glucose uptake (see below)