A fault in a distributed system is a defect in the software or a hardware component which commonly results in errors and failures. Fault tolerance methods provide correct operation of a system in the presence of faults. Redundancy through replication is a basic method for faultFault tolerance tolerance in a distributed system. Process groups are commonly used to provide replication and orderly group communication is needed for correct operation of replicas. In this chapter, we review basic fault tolerance methods, group communication protocols, implement these protocols in Python using mpi4py and describe the consensus problem in distributed systems.