Future wireless networks are envisaged to consist of a variety of integrated and jointly managed radio access technologies (RATs). This is motivated by the complementary features of the individual RATs. When in the overlapping coverage of the integrated RATs, a multimode terminal can use them simultaneously, thus aggregating bandwidth to enhance performance of high-bandwidth applications. However, there are challenges that must be addressed to achieve efficient bandwidth aggregation. Packet reordering is the most dominant challenge. Packet reordering can lead to excessive delays that can affect real-time applications; it can also affect throughput of TCP applications adversely. To circumvent the reordering problem and other challenges associated with simultaneous use of the terminal's multiple interfaces, bandwidth aggregation solutions are developed. This paper reviews existing bandwidth aggregation solutions in heterogeneous wireless networks. Challenges and several open research issues in the design of bandwidth aggregation approaches are also outlined. To the best of our knowledge, this is the first comprehensive review of existing bandwidth aggregation techniques in heterogeneous wireless networks. This paper, therefore, provides important lessons and information from current bandwidth aggregation solutions, which can be used to guide the development of more efficient bandwidth aggregation approaches.