A bstract We study SU( N ) Quantum Chromodynamics (QCD) in 3+1 dimensions with N f degenerate fundamental quarks with mass m and a θ -parameter. For generic m and θ the theory has a single gapped vacuum. However, as θ is varied through θ = π for large m there is a first order transition. For N f = 1 the first order transition line ends at a point with a massless η ′ particle (for all N ) and for N f > 1 the first order transition ends at m = 0, where, depending on the value of N f , the IR theory has free Nambu-Goldstone bosons, an interacting conformal field theory, or a free gauge theory. Even when the 4 d bulk is smooth, domain walls and interfaces can have interesting phase transitions separating different 3 d phases. These turn out to be the phases of the recently studied 3 d Chern-Simons matter theories, thus relating the dynamics of QCD 4 and QCD 3 , and, in particular, making contact with the recently discussed dualities in 2+1 dimensions. For example, when the massless 4 d theory has an SU( N f ) sigma model, the domain wall theory at low (nonzero) mass supports a 3 d massless ℂ ℙ N f − 1 nonlinear σ -model with a Wess-Zumino term, in agreement with the conjectured dynamics in 2+1 dimensions.