Electrochemical
and photoelectrochemical CO2 reduction
technologies offer the promise of zero-carbon-emission renewable fuels
needed for heavy-duty transportation. However, the inert nature of
the CO2 molecule poses a fundamental challenge that must
be overcome before efficient (photo)electrochemical CO2 reduction at scale will be achieved. Optimal catalysts exhibit enduring
stability, fast kinetics, high selectivity, and low manufacturing
cost. Identifying catalytic mechanisms of CO2 reduction
in (photo)electrochemical systems could accelerate design of efficient
catalysts. In recent decades, numerous theoretical studies have contributed
to our understanding of CO2 reduction pathways and identifying
rate-limiting steps. Although a significant body of work exists regarding
homogeneous electrocatalysis for CO2 reduction, this review
focuses specifically on the theory of heterogeneous (photo)electrochemical reduction. We first give an overview of the
relevant thermodynamics and semiconductor physics. We then introduce
important, widely used theoretical techniques and modeling approaches
to catalysis. Recent progress in elucidating mechanisms of heterogeneous
(photo)electrochemical CO2 reduction is discussed through
the lens of two experimental systems: pyridine (Py)-catalyzed CO2 (photo)electrochemical reduction at p-GaP photoelectrodes
and electrochemical CO2 reduction at Cu electrodes. We
close by proposing strategies and principles for the future design
of (photo)electrochemical catalysts to improve the selectivity and
reaction kinetics of CO2 reduction.