To format Dates we use the format(date, format="%Y-%m-%d") function with either the POSIXct (given from as.POSIXct()) or POSIXlt (given from as.POSIXlt())
d = as.Date("2016-07-21") # Current Date Time Stamp
format(d,"%a") # Abbreviated Weekday
## [1] "Thu"
format(d,"%A") # Full Weekday
## [1] "Thursday"
format(d,"%b") # Abbreviated Month
## [1] "Jul"
format(d,"%B") # Full Month
## [1] "July"
format(d,"%m") # 00-12 Month Format
## [1] "07"
format(d,"%d") # 00-31 Day Format
## [1] "21"
format(d,"%e") # 0-31 Day Format
## [1] "21"
format(d,"%y") # 00-99 Year
## [1] "16"
format(d,"%Y") # Year with Century
## [1] "2016"
For more, see ?strptime.