Multiparty Computation (MPC) protocols allow a set of mutually distrustful parties to compute a program without revealing their private inputs. It has been suggested that MPC can be combined with blockchain systems to achieve two goals: 1. Determine cash distribution according to private inputs; 2. Improve fairness of MPC protocols through financial punishments for misbehaving parties. In this talk, we will present an approach to constructing general purpose MPC protocols that can be efficiently combined with blockchain systems and distributed applications, such as gambling, distributed cryptocurrency exchanges and privacy preserving smart contracts. First, we will present a general approach for combining MPC protocols with public verifiability and cheater identification protocols with blockchain based smart contracts in order to achieve the two goals above. Next we will present a new compiler for achieving public verifiability and cheater identification from MPC protocols with certain simpler properties properties given publicly verifiable oblivious transfer and homomorphic commitments. Finally, we will briefly describe novel constructions of such oblivious transfer and commitment protocols that achieve high concrete efficiency. Based joint work with Carsten Baum, Ignacio Cascudo, Ivan Damgård, Rafael Dowsley, Nico Döttling and Irene Giacomelli.