  In this note we review some of the uses of framed quivers to study BPS
invariants of Donaldson-Thomas type. We will mostly focus on non-compact
Calabi-Yau threefolds. In certain cases the study of these invariants can be
approached as a generalized instanton problem in a six dimensional
cohomological Yang-Mills theory. One can construct a quantum mechanics model
based on a certain framed quiver which locally describes the theory around a
generalized instanton solution. The problem is then reduced to the study of the
moduli spaces of representations of these quivers. Examples include the affine
space and noncommutative crepant resolutions of orbifold singularities. In the
second part of the survey we introduce the concepts of defects in physics and
argue with a few examples that they give rise to a modified Donaldson-Thomas
problem. We mostly focus on divisor defects in six dimensional Yang-Mills
theory and their relation with the moduli spaces of parabolic sheaves. In
certain cases also this problem can be reformulated in terms of framed quivers.
