Chitin, being the second most abundant biopolymer after cellulose, has been gaining popularity since its initial discovery by Braconot in 1811. However, fundamental knowledge and literature on chitin and its derivatives from insects are difficult to obtain. The most common and sought-after sources of chitin are shellfish (especially crustaceans) and other aquatic invertebrates. The amount of shellfish available is obviously restricted by the amount of food waste that is allowed; hence, it is a limited resource. Therefore, insects are the best choices since, out of 1.3 million species in the world, 900,000 are insects, making them the most abundant species in the world. In this review, a total of 82 samples from shellfish—crustaceans and mollusks (n = 46), insects (n = 23), and others (n = 13)—have been collected and studied for their chemical extraction of chitin and its derivatives. The aim of this paper is to review the extraction method of chitin and chitosan for a comparison of the optimal demineralization and deproteinization processes, with a consideration of insects as alternative sources of chitin. The methods employed in this review are based on comprehensive bibliographic research. Based on previous data, the chitin and chitosan contents of insects in past studies favorably compare and compete with those of commercial chitin and chitosan—for example, 45% in Bombyx eri, 36.6% in Periostracum cicadae (cicada sloughs), and 26.2% in Chyrysomya megacephala. Therefore, according to the data reported by previous researchers, demonstrating comparable yield values to those of crustacean chitin and the great interest in insects as alternative sources, efforts towards comprehensive knowledge in this field are relevant.