Flux compactification is a method in string and M theory to construct vacua where all scalar fields (moduli) are massive and supersymmetry is broken with a small positive cosmological constant, essential for reproducing real-world physics. This approach implies a "landscape" of string/M theory vacua, potentially containing many candidates for describing our universe. The paper discusses arguments for and against this idea, statistical surveys of the landscape, and testable consequences, such as observable effects of moduli, constraints on early cosmology, and predictions for the scale of supersymmetry breaking. The review covers the qualitative picture of string and M theory compactification, including supersymmetry, heterotic strings, brane models, moduli fields, Calabi-Yau manifolds, and flux compactification. It discusses the cosmological constant problem, spontaneous supersymmetry breaking, the moduli problem, and early universe cosmology. The paper also addresses quantum gravity, the effective potential, and stability, and presents explicit constructions of flux vacua, including type IIb D3/D7 vacua, type IIa flux vacua, and mirror symmetry. The statistical properties of vacua are analyzed, including the scale of supersymmetry breaking, distributions of gauge groups and matter content, Yukawa couplings, and Calabi-Yau manifolds. The paper discusses the interpretation of the landscape, emphasizing the need for statistical reasoning to survey broad classes of vacua. It concludes that while there is no clear evidence against the "null hypothesis" that each vacuum is a valid candidate, the landscape hypothesis is a conservative option that can lead to testable predictions. The paper highlights the importance of understanding the effective potential, the role of early cosmology in determining a measure factor, and the potential for new physics in string/M theory.Flux compactification is a method in string and M theory to construct vacua where all scalar fields (moduli) are massive and supersymmetry is broken with a small positive cosmological constant, essential for reproducing real-world physics. This approach implies a "landscape" of string/M theory vacua, potentially containing many candidates for describing our universe. The paper discusses arguments for and against this idea, statistical surveys of the landscape, and testable consequences, such as observable effects of moduli, constraints on early cosmology, and predictions for the scale of supersymmetry breaking. The review covers the qualitative picture of string and M theory compactification, including supersymmetry, heterotic strings, brane models, moduli fields, Calabi-Yau manifolds, and flux compactification. It discusses the cosmological constant problem, spontaneous supersymmetry breaking, the moduli problem, and early universe cosmology. The paper also addresses quantum gravity, the effective potential, and stability, and presents explicit constructions of flux vacua, including type IIb D3/D7 vacua, type IIa flux vacua, and mirror symmetry. The statistical properties of vacua are analyzed, including the scale of supersymmetry breaking, distributions of gauge groups and matter content, Yukawa couplings, and Calabi-Yau manifolds. The paper discusses the interpretation of the landscape, emphasizing the need for statistical reasoning to survey broad classes of vacua. It concludes that while there is no clear evidence against the "null hypothesis" that each vacuum is a valid candidate, the landscape hypothesis is a conservative option that can lead to testable predictions. The paper highlights the importance of understanding the effective potential, the role of early cosmology in determining a measure factor, and the potential for new physics in string/M theory.