Lattice QCD is a numerical method for solving the complicated dynamics
of QCD in the non-perturbative, low energy regime, allowing computations of the spectrum and strong
interactions of hadrons. To investigate the interactions of these hadrons with the remainder
of the Standard Model (leptons and the electro-weak gauge bosons) and physics beyond the
Standard Model, external operators must be included. This can be done by calculating hadron
matrix elements with explicit operator insertions and generally also using external field techniques.
In this second approach, the properties of hadrons are computed in an appropriate classical background
field (e.g., electroweak) and their modification from the zero external field case determines the quantity
of interest. I will discuss the advantages and disadvantages of this approach giving examples including
the electromagnetic and spin polarisabilities of hadrons and the nuclear modification of parton
distributions (the EMC effect).