In Java classes java.util.Date, java.util.Calendar, java.time.LocalDateTime, java.time.LocalDate and java.time.LocalTime  implements comparable interface for natural ordering. We can sort these objects implements comparable interface as below

Collections.sort(List <Date> list);
Collections.sort(List <Calendar> list);
Collections.sort(List <LocalDateTime> list);
Collections.sort(List <LocalDate> list);
Collections.sort(List <LocalTime> list);

Problem occurred when date in String format and following different format pattern as dd/MM/yyyy or some more patterns then you have to implement Comparator to sort this date text patterns as below

Collections.sort(dateStrList, new Comparator() {
DateFormat f = new SimpleDateFormat("dd/MM/yyyy"); 

@Override public int compare(String o1, String o2) {
 try { 
   return f.parse(o1).compareTo(f.parse(o2)); 
} catch (ParseException e) { 
throw new IllegalArgumentException(e); 
} 
} }); 

To learn Comparator and Comparable check below link.

Java : Comparable Vs Comparator

In below example you will see sorting of date  in text format and objects also.

Example

package com.date;

import java.text.DateFormat;
import java.text.ParseException;
import java.text.SimpleDateFormat;
import java.time.LocalDate;
import java.time.LocalDateTime;
import java.time.format.DateTimeFormatter;
import java.util.ArrayList;
import java.util.Collections;
import java.util.Comparator;
import java.util.List;

public class SortingDate {

public static void main(String[] args) {
 //java 8
sortDateObject();
sortDateText();
}

private static void sortDateText() {
List<String>dateStrList=new ArrayList<String>();
// Date format dd/MM/YYYY
dateStrList.add("03/04/2016");
dateStrList.add("03/01/2016");
dateStrList.add("02/06/2016");
dateStrList.add("02/09/2016");
dateStrList.add("22/09/2016");
dateStrList.add("16/09/2016");
dateStrList.add("03/04/2016");
dateStrList.add("01/08/2017");
dateStrList.add("02/06/2017");
dateStrList.add("02/09/2014");
dateStrList.add("22/09/2018");
dateStrList.add("16/09/2015");

System.out.println("---> Date List Before Sort (dd/MM/yyyy)");
for(String dateStr:dateStrList)
System.out.println(dateStr);

//Sort String Date
Collections.sort(dateStrList, new Comparator<String>() {
DateFormat f = new SimpleDateFormat("dd/MM/yyyy");
    @Override
    public int compare(String o1, String o2) {
    try {
	 return f.parse(o1).compareTo(f.parse(o2));
	} catch (ParseException e) {
	       throw new IllegalArgumentException(e);
	   }
	   }
	});

    System.out.println("---> Date List After Sort (dd/MM/yyyy)");
    for(String dateStr:dateStrList)
    System.out.println(dateStr);

	}

private static void sortDateObject() {
List<LocalDate>dateList=new ArrayList<LocalDate>();
dateList.add(LocalDate.of(2012, 05, 12));
dateList.add(LocalDate.of(2014, 03, 23));
dateList.add(LocalDate.of(2011, 02, 13));
dateList.add(LocalDate.of(2013, 11, 12));
dateList.add(LocalDate.of(2017, 8, 11));
dateList.add(LocalDate.of(2016, 9, 05));

DateTimeFormatter dateTimeFormatter = DateTimeFormatter
				.ofPattern("MM/dd/yyyy");
System.out.println("---> Date  Object List Before Sort (MM/dd/yyyy)");
for(LocalDate localDate:dateList)
{
  System.out.println(localDate.format(dateTimeFormatter));
}
// LocalDate  internally having Comparable interface no need additional Comparator
Collections.sort(dateList);

System.out.println("---> Date Object List After Sort (MM/dd/yyyy)");
for(LocalDate localDate:dateList)
{
System.out.println(localDate.format(dateTimeFormatter));
}

}

}

Output

---> Date  Object List Before Sort (MM/dd/yyyy)
05/12/2012
03/23/2014
02/13/2011
11/12/2013
08/11/2017
09/05/2016
---> Date Object List After Sort (MM/dd/yyyy)
02/13/2011
05/12/2012
11/12/2013
03/23/2014
09/05/2016
08/11/2017
---> Date List Before Sort (dd/MM/yyyy)
03/04/2016
03/01/2016
02/06/2016
02/09/2016
22/09/2016
16/09/2016
03/04/2016
01/08/2017
02/06/2017
02/09/2014
22/09/2018
16/09/2015
---> Date List After Sort (dd/MM/yyyy)
02/09/2014
16/09/2015
03/01/2016
03/04/2016
03/04/2016
02/06/2016
02/09/2016
16/09/2016
22/09/2016
02/06/2017
01/08/2017
22/09/2018