Wind and photovoltaic generation systems possess fluctuating output power due to intermittency in wind speed and solar irradiance which needs to be smoothed before supplying power to the grid for a proper operation. Several power smoothing methods are developed in recent years for wind and photovoltaic systems. This paper presents an extensive review of the output power smoothing methods considering the use of the energy storage system (ESS). In general, the smoothing of fluctuating power is carried out with an ESS such as a battery energy storage system, fuel cell/electrolyzer, superconducting magnetic energy storage, flywheel energy storage system, energy capacitor system as well as without any energy storage system. As the installation and maintenance cost of ESS-based smoothing methods are high, the existing approaches of power smoothing can be broadly categorized into with and without ESS. This paper discusses the merits and demerits of the existing research in power smoothing approaches and proposes key future directions. Moreover, a comparative study of some well-known smoothing techniques is presented for a simple power system with wind, Photovoltaics and batteries.