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Diffusion Models (DMs) have demonstrated state-of-the-art performance in content generation without requiring adversarial training. These models are trained using a two-step process. First, a forward - diffusion - process gradually adds noise to a datum (usually an image). Then, a backward - reverse diffusion - process gradually removes the noise to turn it into a sample of the target distribution being modelled. DMs are inspired by non-equilibrium thermodynamics and have inherent high computational complexity. Due to the frequent function evaluations and gradient calculations in high-dimensional spaces, these models incur considerable computational overhead during both training and inference stages. This can not only preclude the democratization of diffusion-based modelling, but also hinder the adaption of diffusion models in real-life applications. Not to mention, the efficiency of computational models is fast becoming a significant concern due to excessive energy consumption and environmental scares. These factors have led to multiple contributions in the literature that focus on devising computationally efficient DMs. In this review, we present the most recent advances in diffusion models for vision, specifically focusing on the important design aspects that affect the computational efficiency of DMs. In particular, we emphasize the recently proposed design choices that have led to more efficient DMs. Unlike the other recent reviews, which discuss diffusion models from a broad perspective, this survey is aimed at pushing this research direction forward by highlighting the design strategies in the literature that are resulting in practicable models for the broader research community. We also provide a future outlook of diffusion models in vision from their computational efficiency viewpoint.