Making conflicting statements to others, or equivocation, is a simple yet remarkably powerful tool of malicious participants in distributed systems of all kinds. In distributed computing protocols, equivocation leads to Byzantine faults and fairness issues. In this talk, I will cover my recent work towards preventing or penalizing equivocations in decentralized Systems. In the first half of the talk, we study how the resilience of asynchronous distributed computing tasks such as Byzantine agreement and multiparty computation can be improved using an increment-only counter that implements non-equivocation, a mechanism to restrict a corrupted party from making conflicting statements to different (honest) parties. In the second half of the talk, we show how equivocation can be monetarily disincentivized by the use of crypto-currencies such as Bitcoin. To this end, we have designed completely decentralized non-equivocation (smart) contracts, which make it possible to penalize an equivocating party by the loss of its money.