They can do something else.

On page 272 of the 5th edition DMG there are the following options that a 5e referee may use in his campaign.

Overrun

You can force your way through an opponents space by making a Str(Athletic) vs Str(Athletic) check.

Shove Aside

You can use a variant of the shove attack to move an opponent to an empty space within the attacker's reach. Use the rules for shove attack but the attacker has disadvantage.

Tumble

You can tumble you way through an opponent's space by ducking, weaving, ect. As an action or bonus action you make a Dex (Acrobatics) check versus Dex (Acrobatic) check.

They can do something else.

On page 272 of the 5th edition DMG, there are the following options that a 5e DM may allow players to do as actions in their campaign.

Overrun

You can try to force your way through an opponent's space by making a contested Strength (Athletics) vs. Strength (Athletics) check as an action or bonus action. You have advantage on the check if you're larger than the opponent, or disadvantage if smaller. If you succeed, you can move through the enemy's space once this turn.

Shove Aside

You can use a variant of the shove attack to move an opponent 5 feet to an empty space within your reach. Use the rules for shove attack - a contested Strength (Athletics) vs. Strength (Athletics) or Dexterity (Acrobatics) check - but you (the attacker) have disadvantage on your Athletics roll. If you succeed, you move the opponent 5 feet to a different space within your reach.

Tumble

You can try to tumble your way through an opponent's space by ducking, weaving, etc. As an action or bonus action, you can make a contested Dexterity (Acrobatics) check vs. Dexterity (Acrobatics) check. If you succeed, you can move through the enemy's space once this turn.