The main aim of this paper is to describe the problems that confront experimentalists who attempt to determine Newton's constant of gravitation, G. I will motivate this work by discussing the role of Newton's constant of gravitation in classical physics and recent ideas as to its role in quantum physics. I will then discuss some key aspects of a precision determination of G. This will include criteria for the selection of the detector of the gravitational torque from the point of view of random uncertainties due to read-out noise, thermal and vibrational noise. Another important factor in precise determinations of G is the control of systematic effects (type B uncertainties) such as those due to uncertainties in absolute calibration of the gravitational torque, density homogeneity of source masses and length metrology. I will illustrate the discussion using the determination of G currently underway at the International Bureau of Weights and Measures in France, and describe other experimental configurations that have been used in the past or are being currently developed.