Concurrent programs and systems are usually highly efficient and respond faster than serial systems, making them widely used in practice. However, concurrent programs and systems are often prone to error, which could bring fatal consequences in real world applications. Moreover, the non-determinism brought by concurrency is a major difficulty in the verification of concurrent programs. With formal verification, people could use interactive theorem provers to rigorously prove the correctness of a concurrent program. This study presents several correctness criteria for concurrent programs, which can be verified by interactive theorem proof techniques. The criteria include Hoare triple, linearizability, contextual refinement, and logical atomicity. Researchers usually use program logic to verify programs in an interactive theorem prover. This study summarizes the usage of concurrent separation logic, rely-guarantee-based logic, and relational Hoare logic in concurrent program verifications. It also surveys existing foundational verification tools and verification results by these techniques.