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If you know the latex code of a character which you want in unicode, just enter the its code and then press enter. The unicode character is then copied to the clipboard and then automatically pasted to last focused application (e.g. chat window).
If there is no such code found, the advanced converter turns on. The advanced converter supports the latex characters prefixed by a '' and superscripts and subscripts. Super and subscripts are supported only for digits and the +, - and = signs.
Here are several examples which demonstrate what is supported (this is all unicode, no markup):
"α² ⋅ α²⁺³ ≡ α⁷": "\alpha^2 \cdot \alpha^{2+3} \equiv \alpha^7"
"𝐴 ∈ ℝⁿˣⁿ, 𝐯 ∈ ℝⁿ, λ ∈ ℝ: 𝐴𝐯 = λ𝐯": "\itA \in \bbR^{nxn}, \bfv \in \bbR^n, \lambda \in \bbR: \itA\bfv = \lambda\bfv"
"𝐛𝐨𝐥𝐝𝐟𝐚𝐜𝐞 𝑖𝑡𝑎𝑙𝑖𝑐 𝕓𝕝𝕒𝕔𝕜𝕓𝕠𝕒𝕣𝕕 𝓬𝓪𝓵𝓵𝓲𝓰𝓻𝓪𝓹𝓱𝓲𝓬 𝔣𝔯𝔞𝔨𝔱𝔲𝔯 𝚖𝚘𝚗𝚘𝚜𝚙𝚊𝚌𝚎": "\bf{boldface} \it{italic} \bb{blackboard} \cal{calligraphic} \frak{fraktur} \mono{monospace}"
You should bind the application to a hotkey to be able to easily use. For example in Gnome you could do this in the keyboard settings:
The application currently works only on Linux. It uses python, python's tkinter library or GTK depending which is available, xclip and xdotool utilities. You can start the gui on Windows/Mac though as it is cross-platform but auto-pasting isn't supported yet.
Phillip Berndt - made it work under Python 2.7.
Jos van den Oever - his unilatex.vim served as a base for the latex <-> unicode mapping.
vikhyat was kind enough to put up a similar application on his server for online use: http://vikhyat.net/stuff/latex_to_unicode/