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 light).

Defining taste as being limited to five categories suggests that taste is a 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.

The picture is further complicated by recent research which suggests that perceptions of taste are very dependent on other 'multisensory' inputs.

It is clear that different combinations of senses are involved in the various stages of our interaction with food and drink and different neural substrates are involved too. The latest neuroimaging has started to reveal the many factors determining which complex (i.e., real-world) food stimuli we attend to.

[…] researchers have yet to come to any kind of consensus regarding which senses are constitutive of multisensory flavor perception and which other senses merely modulate the experience.

Source : Multisensory Perception From Laboratory to Clinic 2020, Pages 221-237, Multisensory flavor perception: A cognitive neuroscience perspective, by Professor Charles Spence at the Crossmodal Research Laboratory, Department of Experimental Psychology, Oxford University

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 the influence of the sense of smellplugin-autotooltip__plain plugin-autotooltip_bigSense of smell - Olfaction

It's known that humans have about 10 cm2 of olfactory epithelium, with roughly 5 million sensory neurons.

Smells are detected due to the activation of neurons by airborne volatile chemicals and particles. Different chemicals affect different groups of neurons, which, after cerebral processing, lead to the impression of 'smell'. on taste - i.e. flavour perception.

Although it's known that the sense of smell can have an effect on flavour perception, the degree to which it does so in unknown.

It is frequently asserted that somewhere between 75 and 95 % of what we commonly think of as taste actually comes from the sense of smell. However, empirical evidence in support of such a precise-sounding quantitative claim is rarely, if ever, cited. Indeed, a closer look at the study that appears to have given rise to statements of this general type simply does not support the claim as made.

Source : Just how much of what we taste derives from the sense of smell? Flavour (2015) 4:30

The author of the paper above, Professor Charles Spence (see link above), also points out that :

[…] I would be tempted to argue that it is pretty much meaningless to try and put a precise value, or even a narrow range of values, around the relative contribution of olfactory cues to multisensory flavour perception.