Intraseasonal variability (ISV) of sea surface height (SSH) over the Bay of Bengal (BoB) is studied using altimetry data and an eddy‐resolving ocean model. In both the model hindcast and satellite observations, large SSH ISV is found along the eastern and northern coasts of the BoB, in the western BoB, and in a zonal band across the Bay centered near 5°N. The ISV displays a clear seasonality. In the western BoB, it reaches its annual maximum in spring, whereas it does so in summer and autumn southeast of Sri Lanka. Driven by equatorial intraseasonal winds, equatorial Kelvin waves propagate eastward, reach the western coast of Sumatra, and reflect there to propagate around the perimeter of the BoB as coastally trapped waves. Two distinct bands of high eddy activity are detected in the western and central BoB, respectively. In both bands, isolated eddies propagate southwestward. Eddy formation in the eddy train in the central Bay is linked to the coastal wave as it bends around the corner of the Irrawaddy Delta off Myanmar. Eddy activity contributes to the high ISV in the central Bay to some extent. An energetics analysis indicates that high total eddy energy in the western BoB is due to barotropic/baroclinic instability of the mean current. Key Points Large SSH ISV is found along the coasts of the BoB and in the western BoB The coastal Kelvin wave contributes to SSH ISV along the coasts of the BoB Eddy activity and instability of current cause the SSH ISV in the western BoB