Solar oscillation frequencies are normally described by spherical harmonics and have three `quantum' numbers associated with them -- the radial order $n$, the degree $\ell$ and the azimuthal order $m$. In the absence of asphericities, all modes with the same $n$ and $\ell$ have the same frequency and the frequency is determined by the spherically symmetric structure, particularly the sound-speed profile of the Sun. Asymmetry is introduced mainly by rotation and cause the $(n,\ell)$ multiplet to ``split'' into $2\ell +1$ components. Since the mode-frequencies depend on the spherically symmetric structure and the asphericities, they can be inverted to determine these quantities. The total number of modes observed is of the order of $10^6$ and thus inverting these is a computationally challenging task.
In this talk I shall describe some of the common methods used in helioseismic inversions and their limitations, and talk about some of the techniques used to reduce the problem to a manageable form -- both in terms of memory and time required. In particular, I shall show how the ill-conditioned nature of the problem can be exploited to reduce the size of the inversion. I shall also outline some steps where better algorithms will be of help.