Reading assessment should be completed with cognitive skills (memory and rapid automatized naming) and linguistic skills (particularly phonological domain) related to reading and learning to read. This review aims to present the importance of assessing in general and the two aspects of reading assessment in terms of screening and diagnosis. For screening and more precisely to detect children at-risk of failure in learning to read, tests of language development and phonological skills are presented. For a diagnosis in reading, we distinguish pencil-paper tests and computer-based tests. For a complete diagnosis, tests in written word recognition and in reading comprehension are presented with their limits. We conclude that assessment should be closely related to interventions as prevention or remediation.