Generally, there are two expressions of tensors: the integral and the component expressions. However they are both not enough comprehensive and perfect. It is beneficial to extend the concepts of base vectors and vector bases to the concepts of base tensors and tensor bases. These concepts can be derived based on the concept of base vectors and the law of tensor product (outer product) and any tensor can be expressed by the linear sum of the corresponding base tensors. It is also shown that the dyad is just the outer product of two vectors, and the relationship between dyads and tensors can be accordingly set up. Such recognition is of great value for understanding and applying tensor equations of physical laws.