Let \pi(x; q, a) denote the number of primes less than or equal to x that are congruent to a mod q. The Brun-Titchmarsh theorem gives the bound \pi(x; q, a) < (C+o(1))x / \phi(q) log x, where C depends on the ratio log x / log q. In this talk, we will present our recent work on strengthening this inequality for different ranges of log x / log q. Our approach involves various estimates for character and exponential sums, based on arithmetic exponent pairs and bilinear forms with Kloosterman sums, among other tools.