Contract testing: Should or shouldn't?

In teams quite often happens that the API changes and breaks other services, tests, UI. At the same time, everyone uses Swagger, go to meetings and agree on everything. But still, something is breaking.

What are the ways to solve the synchronization problem and API changes? This talk will consider approaches to writing contract tests on Spring Cloud Contract, Pact and even using binary protocols. If you are familiar with contract testing but have used one of the above tools, or if you know nothing about contract testing but face the same problems then after the talk you will definitely know more about possible solutions, and how much they are "expensive".