In this report, I first review the evolution of ideas of causation as it relates to causal inference. Then I introduce two currently competing perspectives on this issue: the counterfactual perspective and the noncounterfactual perspective. The ideas of two statisticians, Donald B. Rubin, representing the counterfactual perspective, and A.P.Dawid, representing the noncounterfactual perspective are examined in detail and compared with the evolution of ideas of causality. The main difference between these two perspectives is that the counterfactual perspective is based on counterfactuals which cannot be observed even in principle but the noncounterfactual perspective only relies on observables. I describe the definition of causes and causal inference methods under both perspectives, and I illustrate the application of the two types of methods by specific examples. Finally, I explore various controversies on these two perspectives.