Two key mechanisms of the Internet are congestion control in the Transmission Control Protocol (TCP) and Active Queue Management (AQM) in routers. The former divides the bandwidth between flows and prevents the Internet from congestion collapse. Simultaneously, the latter informs hosts of the forthcoming congestion by preventive dropping of packets in network nodes. Although these two key mechanisms may severely interact with each other, they are often being researched independently, in parallel. This has led to the development of a few new congestion controls and AQM algorithms known for excellent performance under the assumption that the counterpart remains unaltered. It is unclear, however, how these new solutions in both areas interact with each other. The purpose of this paper is to fill this gap. Namely, in an extensive set of simulations, the impact of interactions between the state-of-the-art congestion control and AQM algorithms on the TCP connection performance is studied. As a result, recommendations for using some particular TCP-AQM pairs, which are observed to perform especially well, are formulated.