A battery-and-handheld-seat assembling structure includes a handheld seat and a battery. A battery-and-charger assembling structure includes a battery and a charger. The battery is detachably mounted on the handheld seat or in the charger. The battery has two first grooves formed on two side surfaces. Each first groove has a transverse segment and a longitudinal segment connected to each other vertically or substantially vertically. The handheld seat has two first assembling segments. The charger has two third assembling segments. The first assembling segments or the third assembling segments are selectively mounted in the two transverse segments respectively. Each of the first assembling segments or each of the third assembling segments engages with or disengages from the corresponding first groove, thereby strengthening the connection between the battery with the handheld seat or the charger.