  We discuss the phenomenology of phase transitions studied with two control
variables. Such measurements have become routine with magnetic field and
temperature being varied for 1st order magnetic transitions with an ease not
conceivable with pressure and temperature. Similar ease may be possible with
electric field as the second control variable, as in current studies on
multiferroics. We develop this phenomenology for broad 1st order transitions
that occur over a range of the control variable, as is common in substitutional
alloys with inherent quenched disorder, including the possibility of a
glasslike arrest of the transition occurring within this range of either
control variable. The interrupted transition then results in the two competing
phases coexisting to the lowest temperature. The new experimental protocol with
acronym CHUF, where the sample is cooled and heated under different values of
the second control variable, allows a detailed study of glasslike arrest of
kinetics of the phase transformation. The many experimental studies on 1st
order magnetic transitions in a large number of materials, that provide the
cause for this phenomenology, shall be discussed subsequently.
