Semiconducting carbon nanotubes (CNTs) have several properties that are advantageous for field effect transistors such as high mobility, good electrostatics due to their small diameter allowing for aggressive gate length scaling and capability to withstand high current densities. However, in spite of the exceptional performance of single transistors only a few simple circuits and logic gates using CNTs have been demonstrated so far. One of the major obstacles for large scale integration of CNTs is to reliably fabricate p-type and n-type ohmic contacts. To achieve this, the nature of Schottky barriers that often form between metals and small diameter CNTs has to be fully understood. However, since experimental techniques commonly used to study contacts to bulk materials cannot be exploited and studies often have been performed on only single or a few devices there is a large discrepancy in the Schottky barrier heights reported and also several contradicting conclusions. This paper presents a comprehensive review of both theoretical and experimental results on CNT-metal contacts. The main focus is on comparisons between theoretical predictions and experimental results and identifying what needs to be done to gain further understanding of Schottky barriers in CNT-metal contacts.