Over the past decade, visible-light photoredox catalysis has blossomed as a powerful strategy and offers a discrete activation mode complementary to thermal controlled reactions. Visible-light-mediated photoredox catalysis also offers exciting opportunities to achieve challenging carbon-carbon and carbon-heteroatom bond formations with excellent chemo-, regio-, or stereoselectivity under mild and ecologically benign conditions. The greater part of photoredox reactions depends on heavy metals like ruthenium(II) or iridium(III) based complexes as photoredox catalysts owing to their strong absorption, long-lived excited-state lifetimes and high oxidation or redox potentials. However, these transition metal complexes are expensive and pose severe drawbacks with respect to large scale application and sustainability. Organic dyes are also commonly used as a low-cost alternative to Ru- or Ir-based complexes. However, they have inferior photostability. Thus, further development of alternative photocatalysts based on copper salts or copper complexes is widely investigated because of their economic and environmental benefits. In recent years, visible-light-mediated direct functionalization of olefins or alkynes to afford a diverse range of organic compounds has received extensive interest from synthetic chemists due to their easy availability and reactivity towards a large number of reactants. In this review, we have highlighted the most recent significant advances that have been made in the use of copper-based photocatalysts for the functionalization of olefins and alkynes with an emphasis on substrate scope, limitations, mechanistic understanding and applications of these reactions. This review covers the literature from 2015 to 2021.