I guess you are talking about three principle reading models. These  models include bottom-up, top-down, and interactive models. These models are used when reading a printed content. The bottom-up is known as the most important reading model. The principle destination of this model is to create the fundamental aptitudes which are identified with syllables, letters, and words in content structure. Regularly, the bottom-up reading model is utilized by starting readers. The second model is top-down handling in cognitive perspective of reading. The most important objective of this model is to develop the part of foundation learning that is available in the printed content. The third model is the interactive model (metacognitive perspective). This model joins both bottom-up and top-down strategies. This model is for accomplished readers who have a firm understanding of reading techniques. For more detail, please do search on these models and go through.

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Are you more interested in second-language reading or first-language reading? I would recommend an interactive reading model, both for people reading in their own language and for people reading in a foreign one. However, it is important to bear in mind the constraints that may prevent someone from transferring L1 reading skills to their L2 reading. One important constraint is language level: second language reading theorists and researchers often refer to the existence of a "linguistic ceiling", that is a language level that will need to be reached for learners to be able to transfer L1 reading skills. Another factor which can impede or slow down transfer is previous learning experience -e.g. a learner who has been taught to read in the target language with reading materials that focus too heavily on either bottom-up or top-down models will find it hard to use the same interactive approach that he might well adopt in his own language.

Books and article that I would recommend for L2 reading are:

-”Interactive Approaches to Second Language Reading” by Carrell,Divine and Eskey: this book was a great help to me when I researched reading skills for my MSc in TEFL around 15 years ago. I have no idea if it is still considered to be up-to-date or indeed if it has been updated.

- “A critical overview of Models of Reading Comprehension with a Focus on Cognitive Aspects” by Shahnazari and Dubaghi. This article examines the top-down models, the bottom-up model and a range of different interactive models. The writers approach reading from the perspective of informed eclecticism: their position is that no model is perfect and something is to be gained from an understanding of all models. As far as I can remember, this article is not only on second-language reading. However, it does offer conclusions for the second-language classroom.

-The Application of First Language Reading Models to Second Language Study- A Recent Historical Perspective by Lally. For me this paper underplays the differences between first and second language reading.Nevertheless, it is a useful overview.

-Reading in a Second Language: Moving from Theory to Practice by Grabe (2009). I haven't read this one, but Grabe is one of the key academics in second-language reading.

-If you intend to write or evaluate reading tests, then Assessing Reading by Alderson is essential reading

-If you wish to explore how learners read via introspective methods  such as on-going or retrosopective think-aloud protocols, I would  recommend Introspective Methods in Second Language Research by Faerch and Kasper. Please note that this is on research methods generally, not specifically on reading.

You will find useful information for English as a Second Language in 

Kalifa, H. & Weir, C. J. (2009). Examining Reading. Studies in Language Testing, 29, CUP:Cambridge

Another useful resource might be this article on specific models of the reading process itself. Check it out.

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3001687/

The responses above are excellent recommendations, so I'd only add the following books 

Bernhardt, E. (2011). Understanding advanced second-language reading. New York: Routledge.

Hedgcock, J. y Ferris, D. (2009). Teaching Readers of English. Students, text and context. New York: Rutledge.

I  am really greatful for the insightful and fruitful answers i got from my colleagues. thanks to all and your cooperation is highly appreciated. 

Dear Eyhab, I did a quick search on Google Scholar and embed the link to the results of the search. It seems as if the context of the reading process that you are interested in may also play a role in the models that explain it.  I hope you have electronic access to  some of the journals - some of them may be accessible from research sites. It may also be worthwhile doing a search on ResearchGate. 

https://scholar.google.co.za/scholar?start=0&q=reading+and+models&hl=en&as_sdt=0,5&as_ylo=2011

Dear Eyhab,

my research interests deal with reading comprehension in freshman students. I suggest you an essential text: Comprehension: a Paradigm for Cognition by Kintsch

The point of view from which I study this theme is a "problematic" one. And for this reason I suggest you also this text: La comprensione come problema from Lucia Lumbelli. In the first chapters the author presents an adequate theoretical framework about models of reading comprehension .

Thank you for your interesting question.

I would like to thank you for your fruitful answer Elisa.

Hello Majmaah,

I'm not 100% sure in what context you ask your question. However, I do believe that for any inquiry into Reading it is of importance to know/understand how reading works in the brain. I authored a science overview article on that, which also carries a lot of source references to allow you to seek further. My article carries a clear reference to Dr. Coltheart's Dual Route Cascaded Model of Reading, which enjoys cientific consensus on how reading works in the brain. His understanding has since been enriched and deepened by new research, but a thorough understanding of his DRC-Model will certainly help you conceptually.

Hope this helps, Majmaah

Just a few that have various models.  You may want to start with the Gough and Tumner one...it is the Simple View of Reading, which has been around a long time and is very prominent.  Also, the Ehri and McCormick is about the development of reading as opposed to being a "model".  Best of luck.

Gough and Tunmer (1986) Decoding, reading, and reading disability

Kintsch (1988) The role of knowledge in discourse comprehension: a construction-integration model.

Perfetti and Stafura (2014) Word knowledge in a theory of reading comprehension

Cromley and Azevedo (2007) Testing and Refining the Direct and Inferential Mediation Model of Reading Comprehension

Ehri and McCormick (1998) PHASES OF WORD LEARNING: IMPLICATIONS FOR INSTRUCTION WITH DELAYED AND DISABLED READERS

Check out the most recent edition of the Theoretical Models and Processes of Reading (6th Ed.by Alvermann, Unrau, and Ruddell (2013) published by the International Reading Association (now the International Literacy Association).