Mobile crowdsensing serves as a critical building block for emerging Internet of Things (IoT) applications. However, the sensing devices continuously generate a large amount of data, which consumes much resources (e.g., bandwidth, energy, and storage) and may sacrifice the Quality-of-Service (QoS) of applications. Prior work has demonstrated that there is significant redundancy in the content of the sensed data. By judiciously reducing redundant data, data size and load can be significantly reduced, thereby reducing resource cost and facilitating the timely delivery of unique, probably critical information and enhancing QoS. This article presents a survey of existing works on mobile crowdsensing strategies with an emphasis on reducing resource cost and achieving high QoS. We start by introducing the motivation for this survey and present the necessary background of crowdsensing and IoT. We then present various mobile crowdsensing strategies and discuss their strengths and limitations. Finally, we discuss future research directions for mobile crowdsensing for IoT. The survey addresses a broad range of techniques, methods, models, systems, and applications related to mobile crowdsensing and IoT. Our goal is not only to analyze and compare the strategies proposed in prior works, but also to discuss their applicability toward the IoT and provide guidance on future research directions for mobile crowdsensing.