Tunneling spectroscopy played a central role in the experimental verification of the microscopic theory of superconductivity in the classical superconductors. In the case of high-temperature superconductors (HTS), the initial attempts to adopt the same approach were hampered by various problems related to the complexity of these materials. The progresses made in synthesizing high quality samples, and the use of scanning tunneling microscopy/spectroscopy (STM/STS) on these compounds allowed to overcome the main difficulties. In this review we present some of the experimental highlights obtained with STM/STS techniques over the last decade. Most of the results confirm the fact that this new class of materials differ noticeably from the conventional BCS superconductors, and provide convincing arguments towards the understanding of the microscopic mechanisms at the origin of high-temperature superconductivity