A model for describing two-body high energy hadron reactions at energies above the resonance region is presented. Although no real theory yet exists, one can give a procedure for obtaining a (possibly correct) description of the amplitudes for any two-body resction (whatever the spins involved, including real and imaginary parts of amplitudes, any helicity flip pi exchange as well as vector and tensor exchanges, etc.). The most important new physical effect involved is using the appropriate t-dependent phase for the vacuum exchange amplitude (the Pomeron''), both in elastic scattering and in describing absorption effects. The Pomeron is not a Regge pole. The model is very simple to formulate and has a reasonable physical interpretation in terms of important unitarity effects and absorption. It allows one to understand the partial successes and the inadequacies of previous approaches such as the dual absorptive model the strong absorption model, the view that some amplitudes have Regge pole behavior while others do not, etc, All the 0/sup -/1/2/sup +/ reactions, np yields pn, and pp yields nn, cross sections, polarizations, and amplitudes; these include all the important kinds of helicity amplitudes for any two-body resctions, Apart from a few places the results are verymore » good; it is argued that the few places where there may be some difficulty are due to effects we have left out rather than to the structure of the model. Although the input Reggeon exchanges are not all exchange degenerate, the phases of the output amplitudes after absorption show a remarkable and unexpected resemblance to what one would expect from exchange degenerate poles, apart from the necessity of having a zero structure related to important absorption corrections, A number of related results, some of which are considered puzzles are discussed (total cross section differences for pi N and KN, the increase in sigma /sub T/(K/sup +/p), crossovers, shrinkage, real parts of elastic amplitudes, polarization single and double zeros, line reversed reactions, pp scattering at the ISR, etc,) and some predictions are given, (auth) « less