Change is a routine in software development. Like any system, libraries also evolve over time. As a consequence, clients are compelled to update and, thus, benefit from the available API improvements. However, some of these API changes may break contracts previously established, resulting in compilation errors and behavioral changes. In this paper, we study a set of questions regarding API breaking changes. Our goal is to measure the amount of breaking changes on real-world libraries and its impact on clients at a large-scale level. We assess (i) the frequency of breaking changes, (ii) the behavior of these changes over time, (iii) the impact on clients, and (iv) the characteristics of libraries with high frequency of breaking changes. Our largescale analysis on 317 real-world Java libraries, 9K releases, and 260K client applications shows that (i) 14.78% of the API changes break compatibility with previous versions, (ii) the frequency of breaking changes increases over time, (iii) 2.54% of their clients are impacted, and (iv) systems with higher frequency of breaking changes are larger, more popular, and more active. Based on these results, we provide a set of lessons to better support library and client developers in their maintenance tasks.