In this essay, I outline some of the essential ingredients of a universal theory of reading acquisition, one that seeks to highlight commonalities while embracing the global diversity of languages, writing systems, and cultures. I begin by stressing the need to consider insights from multiple disciplines including neurobiology, cognitive science, linguistics, socio-cultural, and historical inquiry, although my major emphasis is on a writing systems approach. A theme common to several of these perspectives is the need to attain a level of word reading speed and effortlessness necessary to overcome the severe limitations of human (sequential) information processing thereby allowing the reader to devote maximum cognitive resources to comprehension. I then present the "Combinatorial Model"--a universal theory of learning to read based on the fundamental principle of spoken and written language combinatoriality. This principle ("infinite ends from finite means") makes it possible for children to learn how to decipher (i.e., decode), combine and chunk/unitize a limited and learnable set of rudimentary (typically meaningless) elements such as letters, aksharas, syllabograms, and character components into a nested hierarchy of meaningful higher-order units such as morphemes and words that can be recognized instantly and effortlessly via rapid parallel processing of their constituent elements. Combinatoriality enables an orthography to provide "learnability" and "decipherability" for the novice reader (via "phonological transparency") as well as unitizability and automatizability for the expert (via morphemic transparency). I then elaborate on the (i) dual nature of this model and the "unfamiliar-to-familiar/novice-to-expert" framework, (ii) the unit/s of unitization, and (iii) the dual nature of writing. I liken the development of reading to a tree that grows both upwards and outwards. Vertical growth can be thought of as a universal 3-phase progression from "sub-morphemic," through "morpho-lexical," to "supra-lexical" phases in which later-developing phases do not replace earlier phases but are added in a nested combinatorial hierarchy. Outward growth is conceptualized as a process of knowledge "arborization"--ongoing refinement, elaboration, and diversification. I conclude by noting that, despite important recent advances, our knowledge of learning to read in non-European and non-alphabetic systems is still in its infancy. Current research is over-reliant on English--an outlier orthography--together with a handful of Roman-script Western European languages. This has led reading science to neglect many issues of global significance such as homography, tone, diacritics, visual complexity, non-linearity, linguistic distance, multilingualism, multiscriptism, and more. An appreciation of the specifics of the particular language (or languages) and orthography (or orthographies) a child is learning to read "within the broader context of global linguistic, orthographic, and cultural diversity" is crucial not only for a deeper understanding of learning to read a specific language but for a truly global non-ethnocentric science of reading.