6G wireless networks improve on 5G by further increasing reliability, speeding up the networks and increasing the available bandwidth. These evolutionary enhancements, together with a number of revolutionary improvements such as highprecision 3D localization, ultra-high reliability and extreme mobility, introduce a new generation of 6G-native applications. Such application can be based on, for example, distributed, ubiquitous Artificial Intelligence (AI) and ultra-reliable, low-latency Internet of Things (IoT). Along with the enhanced connectivity and novel applications, privacy and security of the networks and the applications must be ensured. Distributed ledger technologies such as blockchain provide one solution for application security and privacy, but introduce their own set of security and privacy risks. In this work, we discuss the opportunities and challenges related to blockchain usage in 6G, and map out possible directions for overtaking the challenges.