This paper presents a comprehensive review of the k·p theory for two-dimensional (2D) transition metal dichalcogenide (TMDC) semiconductors, focusing on the dispersion of valence and conduction bands at their extrema (K, Q, Γ, and M points) in atomic crystals. The authors use ab initio density functional theory (DFT) calculations to parameterize the essential parts of the k·p Hamiltonians for six TMDC materials: MoS$_2$, MoSe$_2$, MoTe$_2$, WS$_2$, WSe$_2$, and WTe$_2$. They discuss the spin-splitting and spin-polarization of the bands, as well as the vibrational properties of these materials. The k·p theory is then applied to analyze optical transitions in 2D TMDCs over a broad spectral range, including the Van Hove singularities in the band structure at the M points. The paper also discusses the visualization of scanning tunneling microscopy (STM) maps. The authors compare their results with experimental data and highlight the robustness of their findings. The review covers lattice parameters, band-structure calculations, vibrational properties, band-edge energy differences, and spin-splittings, providing a detailed and compact description of the electronic properties of 2D TMDCs.This paper presents a comprehensive review of the k·p theory for two-dimensional (2D) transition metal dichalcogenide (TMDC) semiconductors, focusing on the dispersion of valence and conduction bands at their extrema (K, Q, Γ, and M points) in atomic crystals. The authors use ab initio density functional theory (DFT) calculations to parameterize the essential parts of the k·p Hamiltonians for six TMDC materials: MoS$_2$, MoSe$_2$, MoTe$_2$, WS$_2$, WSe$_2$, and WTe$_2$. They discuss the spin-splitting and spin-polarization of the bands, as well as the vibrational properties of these materials. The k·p theory is then applied to analyze optical transitions in 2D TMDCs over a broad spectral range, including the Van Hove singularities in the band structure at the M points. The paper also discusses the visualization of scanning tunneling microscopy (STM) maps. The authors compare their results with experimental data and highlight the robustness of their findings. The review covers lattice parameters, band-structure calculations, vibrational properties, band-edge energy differences, and spin-splittings, providing a detailed and compact description of the electronic properties of 2D TMDCs.