How can a motor system learn the mechanical properties of the environment with which it interact? We present a point of view that has emerged in the recent years from a combination of physiological, computational and psychophysical studies. This point of view is based upon the idea that the mechanical behavior of the motor system is organized into a set of vector-field primitives that the brain may take advantage of both for generating a variety of actions and for recognizing the mechanical properties of novel mechanical environments. The physiological evidence for these primitives comes from a series of microstimulation experiments performed on spinalized frogs. These experiments revealed the presence within the frog's spinal cord of a set of neural circuits whose activation results into a field of orces acting upon the controlled limb. A crucical finding in these experiment was that the simultaneous activation of two sites results in the vectorial sum of the fields generated by the independent activation of each site. The vector summation property corresponss to requiring that each spinal site behave as a separate and independent module. This chapter will discuss how the brain may generate an entire receptoire of movements by the linear superposition of few force fields. According to this view, complex behaviors are built through an approximation process in which the brain combines the outputs of independent control networks. The same approximation may be applied to represent new mechanical environments to which a limb's controller must adapt. Recent psychophysical experiments have suggested that when subjects must learn to more their arm within an undknown fild of forces, they progressively build an internal model of this field. Here, it is argued that the internal model of the external field may result from the appropriate tuning of elementary control fields. A distinctive aspect of this field-approximation paradigm is that it provides a coordinate-invariant representation of motor control and learning.