  The bottleneck network flow problem (BNFP) is a generalization of several
well-studied bottleneck problems such as the bottleneck transportation problem
(BTP), bottleneck assignment problem (BAP), bottleneck path problem (BPP), and
so on. In this paper we provide a review of important results on this topic and
its various special cases. We observe that the BNFP can be solved as a sequence
of $O(\log n)$ maximum flow problems. However, special augmenting path based
algorithms for the maximum flow problem can be modified to obtain algorithms
for the BNFP with the property that these variations and the corresponding
maximum flow algorithms have identical worst case time complexity. On unit
capacity network we show that BNFP can be solved in $O(\min \{{m(n\log
n)}^{{2/3}}, m^{{3/2}}\sqrt{\log n}\})$. This improves the best available
algorithm by a factor of $\sqrt{\log n}$. On unit capacity simple graphs, we
show that BNFP can be solved in $O(m \sqrt {n \log n})$ time. As a consequence
we have an $O(m \sqrt {n \log n})$ algorithm for the BTP with unit arc
capacities.
