During the last decade, tremendous advances have been observed in the broad field of numerical modelling for geo-electromagnetic applications. This trend received support due to increasing industrial needs, mainly caused by hydrocarbon and ore exploration industry. On the other hand, the increasing reliability and accuracy of data acquisition techniques further spurs this development. In this review, we will focus on advances and challenges in numerical modelling in geo-electromagnetics. We review recent developments in the discrete solution of the 3-D induction problem in the time and frequency domains. Particularly, advantages and disadvantages of the common numerical techniques for solving partial differential equations such as the Finite Difference and Finite Element methods will be considered.