The group B_n of braids on n strands is the fundamental group of the configuration space of n points in the plane. Thus, by considering some fiber bundle over the configuration space and taking the corresponding monodromy homomorphism, one obtains a representation of B_n. In this talk we discuss the following representations, treating each of them as a monodromy homomorphism:

1. Artin representation.
2. Burau representation.
3. Lawrence-Krammer-Bigelow representation (a faithful linear representation of B_n, by a recent result) and, if the time permits,
4. Chen's iterated integral of a canonical formal power series connection, which is the same thing as Kontsevich integral for braids.