The problem concerning the greenhouse effects of human activities has broadened in scope from the CO2-climate problem to the trace gas-climate problem. The climate effects of non-CO2 trace gases are strongly governed by interactions between chemistry, radiation, and dynamics. We discuss in detail the nature of the trace gas radiative heating and describe the importance of radiative-chemical interactions within the troposphere and the stratosphere. We make an assessment of the trace gas effects on troposphere-stratosphere temperature trends for the period covering the preindustrial era to the present and for the next several decades. Non-CO2 greenhouse gases in the atmosphere are now adding to the greenhouse effect by an amount comparable to the effect of CO2. The rate of decadal increase of the total greenhouse forcing is now 3–6 times greater than the mean rate for the period 1850–1960, Time-dependent calculations with a simplified one-dimensional diffusive ocean model suggest that a surface warming about 0.4–0.8 K should have occurred during 1850 to 1980. For the various trace gas scenarios considered in this study, the equilibrium surface warming for the period 1980 to 2030 ranges from 0.8 to 4.1 K. This wide range in the projected warming is due to the range in the assumed scenario as well as due to the threefold uncertainty in the sensitivity of climate models. For the 180-year period from 1850 to 2030, our analysis suggests a trace gas-induced cumulative equilibrium surface warming in the range of 1.5 to 6.1 K. The important non-CO2 greenhouse gases are CFCl3, CF2Cl2, CH4, N2O, O3, and stratospheric H2O. Chlorofluorocarbons (CFCs) (mainly CFCl3 and CF2Cl2), through their indirect chemical effects on O3, have a potentially large stratospheric cooling effect, as large as that due to a CO2 increase. In addition to the direct radiative effect, many of the trace gases have indirect effects on climate. For example, addition of gases such as CH4, CO, and NOx can alter tropospheric O3, which is a radiatively active gas. Within the troposphere the indirect climate effects can be as large as the direct effects. On the other hand, within the stratosphere, temperature changes are largely determined by indirect effects of CFCs. Trace gases can also influence stratospheric H2O through their effect on tropical tropopause temperatures. Furthermore, increases in tropospheric H2O, through the temperature-H2O feedback, can perturb tropospheric chemistry and alter the concentration of CH4 and O3. The fundamental issue that needs to be addressed within the context of the trace gas-climate problem is the relative importance of transport, chemistry, and the indirect effects of trace gases in governing the long-term trends of tropospheric and stratospheric O3, CH4, and stratospheric H2O. Cloud feedback continues to be the major source of uncertainty in the surface temperature sensitivity of climate models. At present, the sign of this feedback is not known. The ocean sequesters the trace gas radiative heating into its interior and thus delays the equilibrium warming. The estimated e-folding time for the approach to equilibrium varies from a few decades to a century and depends nonlinearly on λ−1 and linearly on κ where λ is the climate feedback parameter and κ is the effective ocean thermal diffusivity. The magnitude of λ, which also governs the equilibrium surface warming, is governed strongly by radiative and dynamical processes in the atmosphere, and hence the effect of oceans on transient climate change is determined by the interactions between atmospheric and oceanic dynamical as well as radiative processes. The next crucial issue concerns accurate determination of decadal trends in radiative forcings, trace gases, planetary albedo (to determine effects of aerosols and cloud feedback), and surface-troposphere-stratosphere temperatures. The observational challenges are formidable and must be overcome for a scientifically credible interpretation of the human impacts on climate.