In this dissertation we discuss several properties of codimension-2 branes. We begin by reviewing some of the problems of contemporary theoretical physics, namely the Cosmological Constant and hierarchy problems, discussing some of the attempts made at addressing these problems within the framework of extra-dimensional theories. Next, we give a brief review of the most interesting properties of general codimension-2 branes. We then construct the exact metric for a small Schwarzschild black hole living on a tensional brane, and then generalize the solution to include rotation. These solutions comprise the first known exact solutions describing a black hole on a three-brane. We then discuss the exact metric for a six-dimensional gravitational shockwave, which can be viewed as our brane Schwarzschild black hole boosted to relativistic speed. Finally, after briefly discussing the brane-induced gravity (DGP) model, we reexamine the shockwave solutions in this context when the bulk is infinite. To regulate the short distance singularities in the brane core, we resolve the thin brane by a wrapping a cylindrical 4-brane in a circle, with an axion flux to cancel the vacuum pressure in the compact direction. We discover a large diversity of possible solutions controlled by the axion flux, as governed by its boundary conditions. This shows that brane induced gravity models really give rise to a landscape of vacua, at least semiclassically. We check that we obtain the correct four- and six-dimensional behavior with the crossover scale depending on the value of the tension in an interesting way. In particular, for near-critical branes the crossover scale saturates at the gravitational see-saw scale, independent of the value of the tension on the brane. Finally, we consider fluctuations about the vacuum background in this model, finding that gravity behaves as a Brans-Dicke theory, but contains no ghosts or instabilities.