  Jets are an important probe to identify the hard interaction of interest at
the LHC. They are routinely used in Standard Model precision measurements as
well as in searches for new heavy particles, including jet substructure
methods. In processes with several jets, one typically encounters hierarchies
in the jet transverse momenta and/or dijet invariant masses. Large logarithms
of the ratios of these kinematic jet scales in the cross section are at present
primarily described by parton showers. We present a general factorization
framework called SCET$_+$, which is an extension of Soft-Collinear Effective
Theory (SCET) and allows for a systematic higher-order resummation of such
kinematic logarithms for generic jet hierarchies. In SCET$_+$ additional
intermediate soft/collinear modes are used to resolve jets arising from
additional soft and/or collinear QCD emissions. The resulting factorized cross
sections utilize collinear splitting amplitudes and soft gluon currents and
fully capture spin and color correlations. We discuss how to systematically
combine the different kinematic regimes to obtain a complete description of the
jet phase space. To present its application in a simple context, we use the
case of $e^+e^- \to $3 jets. We then discuss in detail the application to N-jet
processes at hadron colliders, considering representative classes of
hierarchies from which the general case can be built. This includes in
particular multiple hierarchies that are either strongly ordered in angle or
energy or not.
