Tone-sandhi occurs in tonal languages, such as Chinese, when a sequence of tones in words or phrases affect the tones involved. One might say that the tones of the Chinese language will adapt to the tune currently being played.
The three basic rules for tone-sandhi in Mandarin Chinese are:
The character "" (yi1) is pronounced 1) in the 1:st tone when counting, 2) in the 2:nd tone before a syllable with the 4:th tone and 3) in the 4:th tone in all other cases.
The character "" (bu4) is pronounced 1) in the 2:nd tone before a syllable with the 4:th tone and 2) in the 4:th tone in all other cases.
When two or more syllables with the 3:rd tone follow in a row, all but the last syllable will get the 2:nd tone.
Further reading:
Chinese phonetics,
tones 
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