A repetition in a word is a subword with the period at most half of the subword length. We study maximal repetitions occurring in a word, that is those for which any extended subword has a bigger period. The set of such repetitions represents in a compact way all repetitions in the word. We first study maximal repetitions in Fibonacci words -- we count their exact number, and estimate the sum of their exponents. These quantities turn out to be linearly-bounded in the length of the word. We then prove that the sum of exponents of all maximal repetitions in general words of length $n$ (over arbitrary alphabet) is bounded by a linear function in $n$. This implies, in particular, that there is only a linear number of maximal repetitions in a word. We then discuss some algorithmic applications of this result. In particular, we present a linear-time algorithm for finding all maximal repetitions in a word.