Over the past two decades, extensive research has been conducted to explore alternative supplementary cementitious materials (SCMs) in order to address the environmental concerns associated with the cement industry. Bricks, which are frequently preferred in the construction sector, generate a lot of waste during the production and demolition of existing buildings, requiring environmentally sustainable recycling practices. Therefore, many studies have been carried out in recent years on the use of brick waste as supplementary cementitious materials (SCMs) in cement mortar and concrete production. This critical review evaluates the impact of waste brick powder (WBP) on the mechanical and durability properties of mortar and concrete when used as a partial replacement for cement. It was observed that the properties of WBP-blended cement mortar or concrete depend on several factors, including WBP particle size, replacement ratio, pozzolanic activity, and mineralogical structure. The findings indicate that WBP with a particle size range of 100 µm to 25 µm, with a maximum cement replacement level of 10–20%, exhibits a positive impact on the compressive strength of both mortars and concretes. However, it is crucial to emphasize that a minimum curing duration of 28 days is imperative to facilitate the development of a pozzolanic reaction. This temporal requirement plays a vital role in realizing the optimal benefits of utilizing waste brick powder as a supplementary cementitious material in mortars and concretes.