We examine the foundations and implications of constructivism in mathematics and logic, tracing its evolution from classical to modern approaches. We begin by outlining the philosophical and methodological shifts that distinguish constructivism—particularly intuitionism—from classical reasoning. We delve into the Brouwer–Heyting–Kolmogorov (BHK) interpretation, highlighting how it reinterprets traditional proofs. We also address the limitations imposed by intuitionistic principles on widely accepted mathematical constructs such as the Axiom of Choice. Finally, we consider which parts of classical mathematics can be directly translated into constructive terms, focusing on conservativity results, including Glivenko’s Theorem.