Low-power Wide Area Networks (LPWANs) constitute a type of networks which is used to connect things to the Internet from a wide variety of sectors. These types of technologies provide the Internet of Things (IoT) devices with the ability to transmit few bytes of data for long ranges, taking into consideration minimum power consumption. In parallel, IoT applications will cover a wide range of human and life needs from smart environments (cities, home, transportation etc.) to health and quality of life. Among these popular LPWANs technologies, we have identified the unlicensed frequency band (LoRa, DASH7, SigFox, Wi-SUN, etc.), and the licensed frequency band standards (NB-IoT, LTE Cat-M, EC-GSM-IoT, etc.). In general, both types of standards only consider fixed interconnected things, and less attention has been provided to the mobility of the things or devices. In this paper, we address the mobility of the things and the connectivity in each of the three LPWAN standards: LoRaWAN, DASH7, and NB-IoT. In particular, we show how the mobility of things can be achieved when transmitting and receiving data. Then, we provide a general and technical comparison for the three standards. Finally, we illustrate several application scenarios where the mobility is required, and we show how to select the most suited standard. We also discuss the research challenges and perspectives.