Unstable Adams operations are classically defined as a family of self maps of classifying spaces of compact Lie groups.Their importance in homotopy theory and beyond cannot be over-estimated.Unstable Adams operations for compact Lie groups were completely classified by Jackowski McClure and Oliver in the early 1990s.The concept was later generalised to include classifying spaces of p-compact group,and a complete classification was obtain by Anderson,Grodal,Moller and Viruel (for p odd,Anderson-Grodal at the prime 2).More recently Broto,Levi and Oliver introduced p-local compact groups.These are algebraic objects which are modelled on the p-local homotopy theory of classifying spaces of compact Lie groups,and include p-compact groups and some other families of spaces with similarly pleasant properties.A natural question was whether it is possible to define unstable Adams operations on plocal compact groups.This was answered in the positive in a paper by Junod,Levi and Libman,but classification is still an open problem.In this talk I will describe the construction,and some of its properties.Steps towards classification,and the particular difficulties one has to address in the project will also be discussed.