This tutorial review presents theoretical methods for predicting and understanding the optical response of gold nanoparticles. It provides a critical comparison of different approaches, highlighting the effects of retardation in large particles and non-locality in small ones. Far- and near-field spectra are discussed, emphasizing the relevance of near-field effects in surface-enhanced Raman spectroscopy and electron energy-loss spectroscopy. Gold nanoparticles have been used for centuries, but their optical properties were not understood until the 20th century. Maxwell-Garnett and Mie theories explained scattering effects, while Gans' work on ellipsoids predicted color changes. Later, computational methods like the discrete dipole approximation (DDA) and boundary element method (BEM) enabled detailed simulations of nanoparticle responses. Recent advances in computational tools and synthesis techniques have greatly improved understanding and control of nanoparticle optical properties. The optical response of gold nanoparticles is governed by collective electron oscillations, known as plasmons. These produce strong effects in both near- and far-field responses. Far-field properties are described by absorption and scattering cross sections, while near-field properties are crucial for interactions between closely spaced particles and for sensing applications like SERS. For small particles, the non-retarded limit applies, where the electric field dominates. Analytical solutions for spherical and ellipsoidal particles are available, but they fail for larger sizes due to retardation effects. Mie theory accounts for these effects, showing that plasmon resonances shift with particle size and shape. Non-local effects become significant for very small particles, where the local approximation fails. These effects are addressed by modifying the dielectric function to include finite-size corrections. Numerical methods like BEM, DDA, and FDTD are used to solve Maxwell's equations for complex geometries. BEM is efficient for symmetric particles, DDA is suitable for large ensembles, and FDTD is effective for time-resolved simulations. Each method has advantages and limitations in terms of computational speed, memory usage, and versatility. Electron energy-loss spectroscopy (EELS) is a powerful technique for studying near-field interactions, offering high spatial and spectral resolution. It is particularly useful for probing metallic nanoparticles with sub-nanometer resolution. The review highlights the importance of theoretical methods in understanding and predicting the optical behavior of gold nanoparticles, with a focus on their applications in various fields such as plasmonics, sensing, and nanotechnology.This tutorial review presents theoretical methods for predicting and understanding the optical response of gold nanoparticles. It provides a critical comparison of different approaches, highlighting the effects of retardation in large particles and non-locality in small ones. Far- and near-field spectra are discussed, emphasizing the relevance of near-field effects in surface-enhanced Raman spectroscopy and electron energy-loss spectroscopy. Gold nanoparticles have been used for centuries, but their optical properties were not understood until the 20th century. Maxwell-Garnett and Mie theories explained scattering effects, while Gans' work on ellipsoids predicted color changes. Later, computational methods like the discrete dipole approximation (DDA) and boundary element method (BEM) enabled detailed simulations of nanoparticle responses. Recent advances in computational tools and synthesis techniques have greatly improved understanding and control of nanoparticle optical properties. The optical response of gold nanoparticles is governed by collective electron oscillations, known as plasmons. These produce strong effects in both near- and far-field responses. Far-field properties are described by absorption and scattering cross sections, while near-field properties are crucial for interactions between closely spaced particles and for sensing applications like SERS. For small particles, the non-retarded limit applies, where the electric field dominates. Analytical solutions for spherical and ellipsoidal particles are available, but they fail for larger sizes due to retardation effects. Mie theory accounts for these effects, showing that plasmon resonances shift with particle size and shape. Non-local effects become significant for very small particles, where the local approximation fails. These effects are addressed by modifying the dielectric function to include finite-size corrections. Numerical methods like BEM, DDA, and FDTD are used to solve Maxwell's equations for complex geometries. BEM is efficient for symmetric particles, DDA is suitable for large ensembles, and FDTD is effective for time-resolved simulations. Each method has advantages and limitations in terms of computational speed, memory usage, and versatility. Electron energy-loss spectroscopy (EELS) is a powerful technique for studying near-field interactions, offering high spatial and spectral resolution. It is particularly useful for probing metallic nanoparticles with sub-nanometer resolution. The review highlights the importance of theoretical methods in understanding and predicting the optical behavior of gold nanoparticles, with a focus on their applications in various fields such as plasmonics, sensing, and nanotechnology.