The sixth generation (6G) mobile communication networks are expected to intelligently integrate into various aspects of modern digital society, including smart cities, homes, health-care, transportation, and factories. While offering a multitude of services, it is likely that societies become increasingly reliant on 6G infrastructure. Any disruption to these digital services, whether due to human or technical failures, natural disasters, or terrorism, would significantly impact citizens’ daily lives. Hence, 6G networks need not only to provide high-performance services but also to be resilient in maintaining essential services in the face of potentially unknown challenges. This paper provides a general review of the state of the art on resilient systems, definitions, concepts, and approaches. Moreover, it introduces a comprehensive concept, i.e., resilience-by-design (RBD), in three different levels for designing resilient 6G communication networks, summarizing our initial studies within the German Open6GHub project. First, we outline the general RBD enabling principles and discuss their related sub-categories. Next, adopting an interdisciplinary approach, we propose to embed these principles across all 6G layers/perspectives including electronics, physical channel, network components and functions, networks, services, and cross-layer and cross-infrastructure considerations and discuss their challenges. We further elaborate the RBD principles and their realizations along with several 6G use-cases. The paper is concluded by presenting a comprehensive list of open problems for future research on 6G resilience.