Current and future space missions demand highly reliable on-board computing systems, which are capable to carry out high-performance data processing. At present no single computing scheme could efficiently tackle high-performance computing as well as reliability. This paper aims to address that gap. In the first part of the paper, a detailed survey of fault-tolerant distributed computing systems for space applications is presented. Fault types and performance parameters for assessment of a fault-tolerant system are introduced. Redundancy schemes for distributed systems are analysed. A review of the state-of-the-art on fault-tolerant distributed systems is presented and limitations of current approaches are discussed. In the second part of the paper, a new fault-tolerant distributed computing platform with wireless links among the computing nodes is proposed. Novel algorithms, enabling important aspects of the architecture, such as time slot priority adaptive fault-tolerant channel access and fault-tolerant distributed computing using task migration are introduced.