I have used tags in Salesforce classic. Now our project has shifted to lightning and lightning doesn't support tags. Is there any way in lightning through which I can achieve the functionality of Salesforce classic tags.
Edited to reflect that Topics are not fully supported in LEX in Summer 17
Topics are pretty much the new Tags. Topics are part of the standard navigation for Lightning Communities.
It seems like there are a few people talking about how to migrate your old Tags to Topics from back when Topics were introduced:
Sadly, this is not the complete answer as support for them seems to be limited in LEX for internal SF. They are available in the record feed (https://releasenotes.docs.salesforce.com/en-us/summer17/release-notes/rn_chatter_topics_in_lightning.htm), but not on the record page.