Over the years, numerous decipherments have been proposed, but none has been accepted by the scientific community at large. The following factors are usually regarded as the biggest obstacles for a successful decipherment:
The substrate language has not been identified, nor the language family to which it belongs.
The average length of the inscriptions is less than five signs, the longest being one of only 27 signs.
No bilingual texts have been found. Attempts at decipherment
The Russian scholar Yuri V. Knorozov (or Knorosov), who has edited a multi-volumed corpus of the inscriptions, surmises that the symbols represent a logosyllabic script, with an underlying Dravidian language as the most likely linguistic substrate.
If the signs are purely ideographical, they may contain no information about the language spoken by their creators: they would qualify either as a purely logographic script, or as a system of symbols not qualifying as a script in the true sense (pictograms).
Steve Farmer, Richard Sproat, and Michael Witzel
Script vs. ideographical symbols
The topic is popular among amateur researchers, and there have been various (mutually exclusive) decipherment claims. None of these suggestions has found academic recognition to date.
List of decipherment claims:
Clyde Ahmad Winters (Dravidian, 1981)
R. Mathivanan (Tamil, 1991, 1995 Decipherment claims
Onshore explorations near Bet Dwarka in Gujarat revealed the presence of late Indus seals depicting a 3-headed animal, earthen vessel inscribed in a late Harappan script, and a large quantity of pottery similar to Lustrous Red Ware bowl and Red Ware dishes, dish-on-stand, perforated jar and incurved bowls which are datable to the 16th century BC in Dwarka, Rangpur and Prabhas. The thermoluminescence date for the pottery in Bet Dwaraka is 1528 BC. This evidence suggests that a late Harappan script was used until around 1500 BC. have revealed Indus symbols being used as late as 1100 BC.
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Farmer, Steve et al. (2004) The Collapse of the Indus-Script Thesis: The Myth of a Literate Harappan Civilization, EJVS, vol. 11 (2004), issue 2 (Dec)  (PDF).
Knorozov, Yuri V. (ed.) (1965) Predvaritel'noe soobshchenie ob issledovanii protoindiyskikh textov. Moscow.
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Mahadevan, Iravatham, Aryan or Dravidian or Neither? A Study of Recent Attempts to Decipher the Indus Script (1995-2000) EJVS (ISSN 1084-7561) vol. 8 (2002) issue 1 (March 8).
Parpola, Asko (2005) Study of the Indus Script. 50th ICES Tokyo Session.
Possehl, Gregory L. (1996), Indus Age: The Writing System, University of Pennsylvania Press, ISBN 081223345X.
Rjabchikov, Sergei V. (2006a). A New Key to the Proto-Indian Writing System. AnthroGlobe Journal, 2006.
Rjabchikov, Sergei V. (2006b). Protoindiyskoe pis'mo i ego rasshifrovka. Krasnodar.
Subramanian, T. S. (2006) "Significance of Mayiladuthurai find" in The Hindu, May 01, 2006.
Wells, B. "An Introduction to Indus Writing" Independence, MO: Early Sites Research Society 1999.