Due to increasing number of wireless services spectrum congestion is a major concern in both military and commercial wireless networks. To support growing demand for omnipresent spectrum usage, Cognitive Radio is a new epitome in wireless communication that can be used to exploit unused part of the spectrum by dynamically adjusting its operating parameters. While cognitive radio technology is a promising solution to the spectral congestion problem, efficient methods for detecting white spaces in wideband radio spectrum remain a challenge in which secondary users reliably detect spectral opportunities across a wide frequency range. Conventional methods of detection are forced to use the high sampling rate requirement of Nyquist criterion. These are limited in their operational bandwidth by existing hardware devices, much of the extensive theoretical work on spectrum sensing is impossible to realize in practice over a wide frequency band. To lessen the sampling bottleneck, some researchers have begun to use a technique called Compressive Sensing (CS), which allows for the acquisition of sparse signals at subNyquist rates, in conjunction with CRs. In this paper, various wideband spectrum sensing algorithms are discussed along with their merits and limitations and future challenges. Specially, the sub-Nyquist techniques, like compressive sensing and multi-channel sub-Nyquist sampling techniques are concentrated upon.