Particle-in-cell (PIC) methods are widely used in plasma physics for simulating laser-plasma interactions. These methods use a staggered grid for electromagnetic fields and a leapfrog algorithm for particle motion. Modern PIC codes include high-order shape functions, Poisson-preserving field updates, collisions, ionisation, and QED effects. With increased computational power, simulations now use real mass ratios, full 3D dynamics, and multi-speckle interactions. This paper reviews the core algorithms of current PIC codes used in laser-plasma physics, including self-heating rates, collisional convergence, and ionisation tests. It also discusses recent applications in areas such as SRS, short-pulse laser-solid interactions, fast-electron transport, and QED effects. The paper highlights the importance of accurate and convergent PIC algorithms for realistic simulations. It also presents a detailed analysis of the core collisionless PIC algorithm, including the finite-difference time-domain method, particle pusher, and shape functions. The paper also discusses collisions and ionisation, including binary collision operators, ionisation models, and partial superparticle ionisation. It then covers QED effects, including photon emission and pair production, and the inclusion of QED processes in PIC codes. The paper also discusses numerical constraints, such as time-step resolution and macro-particle resolution. Finally, it presents accuracy and convergence tests, including stability and self-heating, and provides heating coefficients for different shape functions. The results show that high-order shape functions significantly reduce self-heating, and that PIC codes are essential for realistic simulations of laser-plasma interactions.Particle-in-cell (PIC) methods are widely used in plasma physics for simulating laser-plasma interactions. These methods use a staggered grid for electromagnetic fields and a leapfrog algorithm for particle motion. Modern PIC codes include high-order shape functions, Poisson-preserving field updates, collisions, ionisation, and QED effects. With increased computational power, simulations now use real mass ratios, full 3D dynamics, and multi-speckle interactions. This paper reviews the core algorithms of current PIC codes used in laser-plasma physics, including self-heating rates, collisional convergence, and ionisation tests. It also discusses recent applications in areas such as SRS, short-pulse laser-solid interactions, fast-electron transport, and QED effects. The paper highlights the importance of accurate and convergent PIC algorithms for realistic simulations. It also presents a detailed analysis of the core collisionless PIC algorithm, including the finite-difference time-domain method, particle pusher, and shape functions. The paper also discusses collisions and ionisation, including binary collision operators, ionisation models, and partial superparticle ionisation. It then covers QED effects, including photon emission and pair production, and the inclusion of QED processes in PIC codes. The paper also discusses numerical constraints, such as time-step resolution and macro-particle resolution. Finally, it presents accuracy and convergence tests, including stability and self-heating, and provides heating coefficients for different shape functions. The results show that high-order shape functions significantly reduce self-heating, and that PIC codes are essential for realistic simulations of laser-plasma interactions.