Slow light in planar photonic structures has attracted for some years an increasing interest due to amazing physical effects it allows or reinforces and to the degrees of freedom it raises for designing new optical functions. Controlling light group velocity is achieved through the use of periodical optical media obtained by nano-structuration of semiconductor wafers at the scale of light wavelength: the so-called photonic crystals. This article reviews present achievements realized in the field of slow light photonic bandgap structures, including the physical principles of slow light to the description of the most advanced integrated optical devices relying on it. Challenges and current hot topics related to slow light are discussed to highlight the balance between the advantages and drawbacks of using slow waves in integrated photonic structures. Then, future trends are described, which is focused on the use of slow wave slot waveguides for nonlinear optics and bio-photonic applications.