  We discuss physical properties of `integer' topological phases of bosons in
D=3+1 dimensions, protected by internal symmetries like time reversal and/or
charge conservation. These phases invoke interactions in a fundamental way but
do not possess topological order and are bosonic analogs of free fermion
topological insulators and superconductors. While a formal cohomology based
classification of such states was recently discovered, their physical
properties remain mysterious. Here we develop a field theoretic description of
several of these states and show that they possess unusual surface states,
which if gapped, must either break the underlying symmetry, or develop
topological order. In the latter case, symmetries are implemented in a way that
is forbidden in a strictly two dimensional theory. While this is the usual fate
of the surface states, exotic gapless states can also be realized. For example,
tuning parameters can naturally lead to a deconfined quantum critical point or,
in other situations, a fully symmetric vortex metal phase. We discuss cases
where the topological phases are characterized by quantized magnetoelectric
response \theta, which, somewhat surprisingly, is an odd multiple of 2\pi. Two
different surface theories are shown to capture these phenomena - the first is
a nonlinear sigma model with a topological term. The second invokes vortices on
the surface that transform under a projective representation of the symmetry
group. A bulk field theory consistent with these properties is identified,
which is a multicomponent `BF' theory supplemented, crucially, with a
topological term. A possible topological phase characterized by the thermal
analog of the magnetoelectric effect is also discussed.
