This paper is a written version of an invited review talk given at the
11th National Quantum Electronics Conference in Belfast in September
1993. It discusses the use of trapped ions for spectroscopy in both th
e optical and microwave regions of the spectrum. After introductory co
mments on the advantages offered by ion traps and laser cooling for sp
ectroscopy, we take the the example of spectroscopy of mercury ions to
show how many different types of experiment can be performed, with st
riking results. We also discuss our recent work at Imperial College, w
hich can be seen as spectroscopy of the ion trap itself, giving inform
ation on the dynamics of the trapped ions.