Standards are specifications to which the elements of a technology must conform. Here, we apply this notion to the biochemical 'technologies' of nature, where objects like DNA and proteins, as well as processes like the regulation of gene activity are highly standardized. We introduce the concept of standards with multiple examples, ranging from the ancient genetic material RNA, to Palaeolithic stone axes, and digital electronics, and we discuss common ways in which standards emerge in nature and technology. We then focus on the question of how standards can facilitate technological and biological innovation. Innovation-enhancing standards include those of proteins and digital electronics. They share common features, such as that few standardized building blocks can be combined through standard interfaces to create myriad useful objects or processes. We argue that such features will also characterize the most innovation-enhancing standards of future technologies.