Chemical analysis of archaeological artefacts is a well-established method for obtaining information on the artefacts and their use. In this thesis, the development and application of novel mass spectrometric methods to archaeological problems is presented. Lipids, being the remains of foods cooked and stored in vessels, are one of the most common classes of molecule analysed, because unglazed vessels can preserve traces of lipids for thousands of years. Analysis is typically carried out by solvent extraction of the lipids followed by gas chromatography-mass spectrometry (GC-MS). However, this is time-consuming. For large ceramic assemblages, of which generally only a small proportion of extracts contain detectable levels of analytes, a medium-throughput screening technique to identify extracts for further analysis would be a great advantage. In addition, GC-based methods are not ideal for large heat-labile molecules such as intact triacylglycerides (TAGs). These molecules are the undegraded remains of the originally deposited fats and their detection is important because TAG distributions can be used to help identify animal species, and to differentiate between dairy and adipose fats. The first part of this thesis presents the development of a method for matrix-assisted laser desorption/ionisation (MALDI)-MS for archaeological lipid extracts, and its application to samples from two archaeological sites. The aim of this work was to develop a method that was better able to detect TAGs than GC-based methods, and that could be used to analyse many samples in a relatively short time. The second part of this thesis presents the detection of opium alkaloids in a Cypriot base-ring juglet from the Late Bronze Age. Although these vessels have long been associated with opium due to their shape, which resembles an inverted poppy capsule, the work presented here is the first robust chemical demonstration of a link between these vessels and their purported use.