We discuss the role of tearing instabilities in magnetic reconnection. In
three dimensions this instability leads to the formation of strong Alfvenic
waves that remove plasma efficiently from the reconnection layer. As a result
the instability proceeds at high rates while staying close to the linear
regime. Our calculations show that for a resistive fluid the reconnection speed
scales as the product of the Alfven speed V_A over the magnetic Reynolds number
to the power -0.3. In the limit of vanishing resistivity, tearing modes proceed
at a non-zero rate, driven by the electron inertia term, giving rise to a
reconnection speed V_A (c/\omega_p L_x)^{3/5}, where \omega_p is the plasma
frequency and L_x is the transverse scale of the reconnection layer. Formally
this solves the problem of fast reconnection, but in practice this reconnection
speed is small.