This paper deals with the dynamics of rising bubbles attached to a vertical wall under different wettability conditions. Even though, bubbles rising freely in a liquid have extensively been studied, bubbles attached to a wall have not been fully understood. Therefore, in this work, rising bubbles attached to a vertical wall were numerically investigated by applying the ALE method along with adaptive mesh refinement schemes to properly resolve the bubble interface and its deformation. To consider wall wettability effects, different contact angles of 45 degrees, 90 degrees, and 105 degrees were considered along with the case of freely rising bubbles. The problem was carried out at different Bond numbers of 0.27, 0.4, and 0.635 for different Reynolds numbers 250, 1000, and 2000. It was shown that in contrast to freely rising bubbles, which have a smooth monotone deformation and motion behavior during the rising, attached bubbles experiences different acceleration/deceleration fields with complicated oscillations and deformations. The results show that wall hydrophobicity strongly affects the bubble profile and consequently the dynamics of bubble rising. In addition, depending on the wall wettability and Bond numbers, the wall-bounded bubbles are influenced by different forces leading to different profiles and hence rise up with different velocities along the wall. The results illustrate that bubbles with contact angles less than 90 degrees move with a speed even higher than freely rising bubbles. (C) 2018 Elsevier Ltd. All rights reserved.