In this paper, we argue that there are foundational dilemmas in theoretical physics related to the concept of reality and the nature of mathematics in physics. Physical theory is treated as a conceptual organism which develops under the weight of its internal contradictions. The paper discusses in depth the problem of objective reality in physics and its relation to scientific practice. Then, it explores the problematic relation between physical meaning and mathematics in modern physical theory, followed by a discussion of the trend of contemporary physics to replace physical principles with pure mathematical principles. Finally, it discusses the problem of logical coherence in modern physical theory. The paper emphasizes the importance of resolving these dilemmas to the proper practice of theoretical physics.