Magnesium (Mg) alloys have great potential in biomedical applications due to their incomparable properties regarding other metals, such as stainless steels, Co–Cr alloys, and titanium (Ti) alloys. However, when Mg engages with body fluids, its degradation rate increases, inhibiting the complete healing of bone tissue. For this reason, it has been necessary to implement protective coatings to control the rate of degradation. This review focuses on natural biopolymer coatings used on Mg alloys for resorbable biomedical applications, as well as some modification techniques implemented before applying natural polymer coatings to improve their performance. Issues such as improving the corrosion resistance, cell adhesion, proliferation, and biodegradability of natural biopolymers are discussed through their basic comparison with inorganic-type coatings. Emphasis is placed on the expected biological behavior of each natural polymer described, to provide basic information as a reference on this topic.