What are the functions of insulin and glucagon for the blood glucose control?

Glucagon enhances glycemia and insulin reduces it. They are antagonistic pancreatic hormones. Glucagon acts stimulating glycogenolysis and therefore forming glucose from glycogen breaking. Insulin is the hormone responsible for the entrance of glucose from the blood into the cells.

When glycemia is low, for instance, during fasting, glucagon is secreted and insulin is inhibited. When glycemia is high, as after meals, there are inhibition of glucagon and more secretion of insulin.

The Endocrine System - Image Diversity: insulin molecule glucose uptake