In this note, we study consensus problems for continuous-time multi-agent systems in directed networks with dynamically changing topologies and nonuniform time-varying delays. We have analyzed consensus problems in the following three cases: 1) directed networks with dynamically changing topologies and nonuniform time-varying delays; 2) directed networks with intermittent communication and data packet dropout; and 3) finite-time consensus in directed networks with dynamically changing topologies and nonuniform time-varying delays. We propose a new approach based on a tree-type transformation to investigate consensus problems in all three cases. Some necessary and/ or sufficient conditions are established. Simulation results are also given to demonstrate the theoretical results.