Neural investigations suggest that there are three possible core deficits in dyslexia: phonemic, grapho-phonemic, and graphemic. These investigations also suggest that the phonemic deficit resides in a different mode of speech perception which is based on allophonic (subphonemic) units rather than phonemic units. Here we review the results of remediation methods that tap into each of these core deficits, and examine how the methods that tap into the phonemic deficit might contribute to the remediation of allophonic perception. Rernediation of grapho-phonemic deficiencies with a new computerized phonics training program (GraphoGame) might be able to surpass the limits of classical phonics training programs, particularly with regard to reading fluency. Remediation of visuo-graphemic deficiencies through exposure to enhanced letter spacing is also promising, although children with dyslexia continued to read more slowly than typical readers after this type of training. Remediation of phonemic deficiencies in dyslexia with programs based solely on phonemic awareness has a limited impact on reading. This might be due to the persistence of a covert deficit in phonemic perception. Methods based on slowed speech enhance the perception not only of phonemic features but also of allophonic features, and this is probably why they have not been found to be effective in meta-analyses. Training of phonemic perception with a perceptual fading paradigm, a method that improves precision in identification and discrimination around phonemic boundaries, has yielded promising results. However, studies with children at risk for dyslexia and dyslexic adults have found that even when behavioral data do not reflect allophonic perception, it can nevertheless be present in neural recordings. Further investigations should seek to confirm that the perceptual fading paradigm is beneficial for reading, and that it renders perception truly phonemic.