The article reviews a theory of a compressible Fermi-liquid-like state at Landau level filling factors \(\nu = 1/q\) or \(1 - 1/q\), where \(q\) is even. The theory explains the quantum Hall effect (QHE) and the fractional quantum Hall effect (FQHE) at these fillings, including the "odd denominator rule." Laughlin's states at \(\nu = 1/q\) and the hierarchical extension to all \(\nu = p/q\) with \(q\) odd are discussed, along with the novel elementary excitations called quasiparticles. The author explores two approaches: one based on trial wavefunctions and the other field theoretical. The field theoretical approach involves representing electrons as \(q\) flux tubes attached to other particles, which can be bosons or fermions depending on \(q\). The mean-field approximation is used to derive the compressible Fermi liquid-like state, and the dynamics of quasiparticles are analyzed. The article also discusses the implications for the FQHE at half-filling and recent experimental observations supporting the theory. Open questions include the effective mass at half-filling and the behavior of the Fermi liquid theory under fluctuations.The article reviews a theory of a compressible Fermi-liquid-like state at Landau level filling factors \(\nu = 1/q\) or \(1 - 1/q\), where \(q\) is even. The theory explains the quantum Hall effect (QHE) and the fractional quantum Hall effect (FQHE) at these fillings, including the "odd denominator rule." Laughlin's states at \(\nu = 1/q\) and the hierarchical extension to all \(\nu = p/q\) with \(q\) odd are discussed, along with the novel elementary excitations called quasiparticles. The author explores two approaches: one based on trial wavefunctions and the other field theoretical. The field theoretical approach involves representing electrons as \(q\) flux tubes attached to other particles, which can be bosons or fermions depending on \(q\). The mean-field approximation is used to derive the compressible Fermi liquid-like state, and the dynamics of quasiparticles are analyzed. The article also discusses the implications for the FQHE at half-filling and recent experimental observations supporting the theory. Open questions include the effective mass at half-filling and the behavior of the Fermi liquid theory under fluctuations.