Business processes define workflows by structuring sets of activities according to given objectives. Process Modeling Languages (PMLs) provide graphical elements to define process models. Apart from use cases in finance and commerce, PMLs gain popularity in application domains such as Cyber-Physical Systems, the Internet of Things, ubiquitous computing, mobile devices, and scenarios happening in rural, restricted, or disaster-affected regions. Many of the domains are exposed to delayed, intermittent, or broken connectivity. Existing PMLs show limitations in considering connectivity-related issues, leading to failures and breakdowns at process runtime. This thesis addresses connectivity-related issues regarding the modeling and execution of resilient business processes taking place in unreliable communication environments. With resilient BPMN (rBPMN), an extension for the Business Process Model and Notation (BPMN) addressing environments with delayed, intermittent, or broken connectivity is introduced. rBPMN extends the BPMN metamodel by new elements for resilient process models. Domain experts may define alternatives for possibly failing message flows based on priorities or characteristics of the alternatives. Functionality offered by remote participants may be moved to other participants for local execution. This thesis illustrates approaches for the graph-based analysis of business processes regarding their resilient operation. By translating process models into directed graphs, graph algorithms allow to dynamically find the most suitable process path. Domain experts are enabled to identify non-resilient parts of a process model, allowing them to optimize the involved segments before runtime. Multi-criteria analysis approaches optimize process operation according to a chosen set of criteria. A real-world scenario of an environmental-friendly slurry application illustrates the use of rBPMN’s concepts and approaches for modeling and executing resilient processes. Technical approaches realizing rBPMN’s resilience strategies using a BPMN runtime engine and microservices are illustrated. The proof-of-concept implementations may be extended and adapted, serving as guides for other application domains.