  I study the two-dimensional defects of the $d$ dimensional critical $O(N)$
model and the defect RG flows between them. By combining the
$\epsilon$-expansion around $d = 4$ and $d = 6$ as well as large $N$
techniques, I find new conformal defects and examine their behavior across
dimensions and at various $N$. I discuss how some of these fixed points relate
to the known ordinary, special and extraordinary transitions in the 3d theory,
as well as examine the presence of new symmetry breaking fixed points
preserving an $O(p) \times O(N-p)$ subgroup of $O(N)$ for $N \le N_c$ (with the
estimate $N_c = 6$). I characterise these fixed points by obtaining their
conformal anomaly coefficients, their 1-point functions and comment on the
calculation of their string potential. These results establish surface
operators as a viable approach to the characterisation of interface critical
phenomena in the 3d critical $O(N)$ model.
