A Wireless Sensor Network (WSN) consists of spatially distributed autonomous sensors. WSNs are vulnerable to security attacks due to the broadcast nature of radio transmission. This paper provides a study of different types of security attacks in WSNs. The focus has been on the sleep deprivation torture (denial-of-sleep) attack which is a type of Denial-of-Service (DoS) attack. The sleep deprivation torture attack aims at preventing a sensor from sleeping thus draining its battery more quickly than it would be under normal usage. A brief study on related works carried out on this attack is also presented.