Why univariate Cox does not have its own survival curve and has to use KM curve as approximation? I am aware that KM-estimator and Cox model use different method. However, I am under the impression that we show KM curve as approximation of univariate Cox model. My question is why univariate Cox does not have its own survival curve?
 A: By default survival curves can’t be drawn from Cox regression because the Cox Proportional Hazards model does not estimate the baseline hazard function (the baseline hazard term cancels out in the partial likelihood function and is ignored when estimating model coefficients). The baseline hazard function is required to plot survival curves. For many scenarios this is fine as we are usually interested in the relative hazard ratio for a prognostic factor and survival, which does not require knowledge of the baseline hazard. 
If you want to show survival curves from a Cox model, often called adjusted survival curves, there are many software packages in R that will draw the curves. These software packages use some method to estimate the baseline hazard function from the data used to fit the Cox model. The Kaplan Meier and Breslow estimators are common choices and usually the user can pick which method to use.
I’ve seen some debate as to whether adjusted or unadjusted survival curves are preferred, so I think it’s important to ask yourself what you’re trying to visualize. If you have a multivariable Cox model with many predictors (especially some that are continuous), I believe it makes more sense to show marginal effects plots for each variable. If you are analyzing an RCT and comparing treatment vs control arm, it then makes more sense to show the survival curve. In this case you can simply use the Kaplan Meier estimator. 
Survival curves are good for showing the survival differences in a few groups, but bad for showing survival for a continuous variable because you’ll be required to dichotomize the variable. If analyzing a continuous variable, skip the survival curve and just show the marginal effects plot. 
