Current theory lists five main taste receptor categories : sweetness, bitterness, sourness, saltiness, and umami. source Wikipedia.
The physical mechanisms for detection of each of these main flavour types have been extensively investigated, and the corresponding tongue 'receptors' have (mostly) been identified.
A common misconception, however, is that any taste can therefore be described as a mixture of these elements (in the way that any visible colour can be formed by mixing red / green / blue).
“Defining taste as being limited to five categories suggests that taste is s simple sensation: this is not true.[…] How each taste is recognised, specificity by taste cells, and how tastes are coded and interpreted are still largely unknown.” source Flavor Chemistry and Technology, Second Edition, p.3, introduction
Even adding-in other taste sensations such as pungency, coolness, astringency,'metallicness', fattiness, and 'heartiness' (kokumi), the mechanisms by which highly complex mixtures of chemicals (e.g. chocolate) can be readily identified and classified are still a mystery.
Update Sep. 2016. A new study performed at Oregon State University suggests that a new 'basic taste' category might be added to the list -'Starchy'. Info. here at New Scientist.
More accurately, the full paper describes experiments in which some people were able to taste glucose oligomer preparations (average degree of polymerization 7 and 14) - and a subsequent focus-group agreed to describe the taste as 'starchy'.
• Note regarding smell. The current estimates for the number of smells that humans can identify could be in the region of 1 Trillion. The figures are currently under dispute. See : The number of olfactory stimuli that humans can discriminate is still unknown eLife. 2015; 4: e08127.