Distributed computing infrastructures support system and network fault-tolerance, e.g., grids and clouds. They transparently repair and prevent communication and system software errors. They also allow duplication and migration of jobs and data to prevent hardware failures. However, only limited work has been done so far on application resilience, i.e., the ability to resume normal execution after errors and abnormal executions in distributed environments. This paper addresses issues in application resilience, i.e., fault-tolerance to algorithmic errors and to resource allocation failures. It addresses solutions for error detection and management. It also overviews a platform used to deploy, execute, monitor, restart and resume distributed applications on grids and cloud infrastructures in case of unexpected behavior.