Pseudorandom binary sequences play a crucial role in cryptography. The classical approach to pseudorandomness of binary sequences is based on computational complexity. This approach has certain weak points thus in the last two decades a new, more constructive and quantitative approach has been developed. Since multidimensional analogs of binary sequences (called binary lattices) also have important applications thus it is a natural idea to extend this new approach to the multidimensional case. This extension started with a paper published in 2006, and since that about 25 papers have been written on this subject. Here our goal is to present a survey of all these papers. (C) 2015 Elsevier B.V. All rights reserved.