Ablation threshold experiments on various materials are carried out using a picosecond laser generating second harmonic radiation in air at atmospheric pressure. Various materials are investigated which vary according to their different electronic band gap structure and include: silicon, fine grain polycrystalline diamond, copper, steel and tungsten carbide. Through the use of scanning electron microscopy and 3D confocal microscopy, the crater depth and diameter are determined and a correlation is found. The ablation thresholds are given for the aforementioned materials and compared with recent literature results. Picosecond laser-material interactions are modelled using the two-temperature model, simulated and compared with experimental results for metallic materials. An extension of the two-temperature model to semiconducting and insulating materials is discussed. This alternative model uses multiple rate equations to describe the transient free electron density. Additionally, a set of coupled ordinary differential equations describes the processes of multiphoton excitation, inverse bremsstrahlung, and collisional excitation. The resulting electron density distribution can be used as an input for an electron density dependent twotemperature model. This multiple rate equation model is a generic and fast model, which provides important information like ablation threshold, ablation depth and optical properties.