This paper presents a review of differences and similarities of in-tube heat transfer and pressure drop between ammonia ($NH_3$) and carbon dioxide ($CO_2$) from the perspective of the design of heat exchangers for $NH_3$ two-stage and $CO_2/NH_3$ cascade refrigeration systems. The focus is on differences in thermophysical properties and thus different characteristics of heat transfer and pressure drop. A brief summary of published literatures about $CO_2/NH_3$ cascade refrigeration systems is provided and literature review of available correlations and developed correlations are presented for flow boiling and condensation heat transfer and pressure drop. Because of large deviation of calculated values with exiting correlations from measured results, a new correlation to predict flow condensation heat transfer coefficients was developed based on experimental results for $CO_2$ at $-15^{circ}C$. From comparison of measured and predicted values, it is shown that some correlation previously published in open literature, can be used to calculate flow boiling heat transfer coefficients for $NH_3$ at $-20^{circ}C$, if a flow pattern can be appropriately determined for a flow condition Also, it is presented that existing correlations can predict well the heat transfer coefficients for $CO_2$ flow boiling at -15 and $-30^{circ}C$. It is shown that some correlations can predict press drop relatively well for $NH_3$ and $CO_2$ two-phase flow. The $NH_3$ and $CO_2$ flow evaporation heat transfer and pressure drop characteristics at $-40^{circ}C$ are compared with predicted values.