Advances in hardware design and manufacturing often lead to new ways in which problems can be solved computationally. In this thesis we explore fundamental problems in three computational models that are based on such recent advances.

The first model is based on new chip architectures, where multiple independent processing units are placed on one chip, allowing for an unprecedented parallelism in hardware. We provide new scheduling algorithms for this computational model.

The second model is motivated by peer-to-peer networks, where countless (often inexpensive) computing devices cooperate in distributed applications without any central control. We state and analyze new algorithms for load balancing and for locality-aware distributed data storage in peer-to-peer networks.

The last model is based on extensions of the streaming model. It is an attempt to capture the class of problems that can be efficiently solved on massive data sets. We give a number of algorithms for this model, and compare it to other models that have been proposed for massive data set computations.

Our algorithms and complexity results for these computational models follow the central thesis that it is an important part of theoretical computer science to model real-world computational structures, and that such effort is richly rewarded by a plethora of interesting and challenging problems.