Burnt Offerings and Sacrifices

Ever since the most ancient of times human beings have offered up sacrifices to the god or gods they served, worshiped, and believed in. But most importantly the prophet Samuel would reveal that to obey God is better than sacrifice (I Samuel 15:22). So what exactly was the sacrificial system like during the era of the Old Testament, and do Orthodox Christian priests offer up bloodless sacrifices in the era of the New Testament?