The core concept in acquisition of reading is phonological coding. However other cognitive processes not directly related to reading influence reading acquisition and may explain reading disability. General intelligence as measured by standardised IQ-type tests does not seem to be relevant either for explaining specific reading disability or individual differences in reading. How can we characterise these cognitive processes within a model of cognitive functions? What is the evidence that, consistent with the model, the designated processes can predict reading competence even among prereaders? The paper will present a theoretical discussion and some empirical results pertaining to the above issues.