Recipe to compute dimension and decompose product of $SO(N)$ group representations

Question

As it is well known Young tableaux (YT) provide an efficient and very useful way to treat $SU(N)$ representation. This is principally based on these facts:

1. There is a correspondence between irreps of $SU(N)$ and YT;

2. There is an easy way to compute dimension of a certain irrep of $SU(N)$ (using again YT);

3. There is an easy algorithm to multiply two or more irreps of $SU(N)$ in terms of YT;

Questions: Is there a way to do the same (points 1. 2. 3.) with $SO(N)$? What are the algorithms to do that?