This review examines observations of magnetic fields in molecular clouds, that is, at spatial scales ranging from tens to tenths of parsecs and densities up to hundreds of particles per cubic centimetre. I will briefly summarize the techniques for observing and mapping magnetic fields in molecular clouds. I will review important examples of observational results obtained using each technique and their implications for our understanding of the role of the magnetic field in molecular cloud formation and evolution. Finally, I will briefly discuss the prospects for advances in our observational capabilities with telescopes and instruments now beginning operation or under construction.