We investigate the problems of resilient cluster consensus in directed networks under three types of multi-agent dynamics, namely, continuous-time multi-agent systems, discretetime multi-agent systems, and switched multi-agent systems composed of both continuous-time and discrete-time components. Resilient cluster censoring strategies are proposed to ensure cluster consensus against locally bounded Byzantine nodes in a purely distributed manner, where neither the number/indentity of Byzantine nodes nor the division of clusters is assumed. We do not require complicated algebraic conditions or any balance conditions over inter-cluster structures, distinguishing the current work from previous results on cluster consensus problems besides a fortiori the attack-tolerant feature. Sufficient conditions are established in all the three scenarios based on the graph robustness. Furthermore, we solve the heterogenous cluster robustness problems and resilient scaled cluster consensus problems as extensions. The theoretical results are illustrated through numerical examples including the Santa Fe collaboration network.