Optical trapping describes the interaction between light and matter to manipulate micro-objects through momentum transfer. In the case of 3D trapping with a single beam, this is termed optical tweezers. Optical tweezers are a powerful and non-invasive tool for manipulating small objects, which have become indispensable in many fields, including physics, biology, soft condensed matter, amongst others. In the early days, optical trapping were typically used with a single Gaussian beam. In recent years, we have witnessed the rapid progress in the use of structured light beams with customized phase, amplitude and polarization in optical trapping. Unusual beam properties, such as phase singularities on-axis, propagation invariant nature, have opened up novel capabilities to the study of micromanipulation in liquid, air and vacuum. In this review, we summarize the recent advances in the field of optical trapping using structured light beams.