Modern computer systems are characterized by having a hierarchical memory organization. During the last decades several computational models have been suggested to integrate characteristITCS of hierarchical memory into the design of algorithms. Many of these models have only had limited success - in the sense that they have been applied only to a few algorithmic problems - but two models have received considerable attention. Aggarwal and Vitter in 1987 suggested the two-level I/O model, that focuses on the number of blocks of data transfered between two memory levels. This is motivated by the fact that in many computations the bottleneck is the block transfers between two adjacent memory levels, where the characteristITCS of the two memory levels are known to the algorithm. This model was generalized by Frigo, Leiserson, Prokop and Ramachandran in 1999, who introduced the simple but powerful ideal-cache model as a formal model of computation for developing algorithms in environments with multiple unknown memory levels. Frigo et al. coined the terminology of "cache-oblivious algorithms". In this talk we will introduce the basic ideas and techniques used when designing cache-oblivious algorithms, survey recent results within the area, and discuss current trends within the area.