In this thesis we study the self-assembly, stability and photonic properties of colloidal photonic crystals. We show that stable photonic crystals can be self-assembled using spherical colloidal particles interacting with a simple pair potential. We focus on two-dimensional quasi-periodic crystals and three-dimensional periodic crystals. For this, we use a core-corona model of the particles which is simulated as particles interacting with a purely repulsive hard-core square-shoulder potential. The first part of the thesis is dedicated to a quasicrystal with dodecagonal (12-fold) symmetry. Here, we find that this quasicrystal is thermodynamically stable, is robust to variations in the shape and size of the interaction potential, and can be formed during sedimentation of colloidal particles. In the second part of the thesis, we identify a range of stable two-dimensional structures at different shoulder widths, namely a stripe phase, a honeycombs lattice, a two-dimensional sigma phase and quasicrystals with 10- and 18- fold symmetries. In the third and last part of the thesis, we analyse the photonic properties of different structures studied in the first two parts. Firstly, we show that the two-dimensional dodecagonal quasicrystal displays a photonic band gap. Secondly, we observe the formation of a novel and stable two-length scale pyrochlore structure displaying a photonic band gap in the three-dimensional system.