A review paper presents a critical examination of the prevailing theories of the threshold transition of injection lasers. The theories are examined for their correspondence with the familiar properties of an oscillator, in particular the appearance of coherence at threshold and the maintenance of the stimulated output with no spontaneous input. The connections are examined between the currents at (a) the knee of the power-current curve P(I); (b) the peak of d(ln P)/d I; (c) the peak of P N, the amplitude of the low frequency power spectrum from the optical detector; and (d) the threshold of oscillation. All theories predict the knee at total current equal to I 0, the component of the current due to spontaneous emission alone at gain equals loss. The cause is the abrupt change in external efficiency when the stimulated power becomes important. The linear rate equations produce neither coherence nor self-sustained oscillation; and in spite of assertions to the contrary, the finite strength of the pump does not give a change in shape of P N(I) near I 0. Three nonlinear models are examined; (1) The van der Pol equation, (2) the rate equations with nonlinearity described by a critical intensity, and (3) those based on a critical power. All three display the properties expected of an oscillator. The sharp maximum in d(ln P)/d I locates the onset of coherence, and the separation between I 0 and the current at the peak depends on the strength of the nonlinearity. Only a very weak nonlinearity is required to move the peak from the infinite current of the linear theory to the observed close coincidence with I 0. The trace of P N(I) shows the location of threshold, but the approximation of the theories is too crude to give the shape in the lasing region. Published experimental data show that the linear theory does not describe the lasing transition nor the behavior at or above threshold. For lack of a mathematical solution in this region, it is not a logical base for perturbation calculations of lasing properties. The experimental evidence on the strength of the nonlinearity is examined and also the empirical distinction between the non-linear rate equations (2) and (3). An Appendix discusses the physical nature of the nonlinearity, and another presents the theory connecting the power spectrum of the detector current to the spectrum of the incident light.