  We review some recent results concerning the properties of a spherically
symmetric global monopole in $(D=d+2)$-dimensional general relativity. Some
common features of monopole solutions are found independently of the choice of
the symmetry-breaking potential. Thus, the solutions show six types of
qualitative behavior and can contain at most one simple horizon. For the
standard Mexican hat potential, we analytically find the $D$-dependent range of
$\gamma$ (the gravitational field strength parameter) in which there exist
globally regular solutions with a monotonically growing Higgs field, containing
a horizon and a Kantowski-Sachs (KS) cosmology outside it, where the topology
of spatial sections is $\R\times \S^d$. Their cosmological properties favor the
idea that the standard Big Bang might be replaced with a nonsingular static
core and a horizon appearing as a result of some symmetry-breaking phase
transition on the Planck energy scale. We have also found families of new
solutions with an oscillating Higgs field, parametrized by the number of its
knots. All such solutions describe space-times of finite size, possessing a
regular center, a horizon and a singularity beyond it.
