How to calculate Implied Volatility for out-of-the-money options?

I'm trying to calculate the implied volatility for out-of-the-money options, and to a lesser extent, in-the-money options. Most of the literature estimations I could find for implied volatility were for at-the-money options.

In other words, given $C(s,t)$, $S$, and $Ke^{-r(T-t)}$, related by:

$$C(s,t) = SN(d_1) - N(d_2)Ke^{-r(T-t)}$$ $$d_1 = \frac{1}{\sigma\sqrt{T-t}}\left(\log(S/K)+\left(r+\frac{\sigma^2}{2}\right)\left(T-t\right)\right)$$ $$d_2 = d_1 - \sigma\sqrt{T-t}$$

I'm trying to calculate $\sigma$. My preliminary investigations have revealed no closed-form solution, so I've resolved to a numerical approximation instead, but I haven't found any literature results on this approximation.

I would be glad if anyone could refer me to any useful approximations or other results. Other comments on this are also welcome as it's a tricky topic.