There are many mayonnaise substitutes available that are healthier than this popular condiment, including vegan options. Mayonnaise is traditionally made by whipping an oil into raw egg yolks and adding vinegar or other acids. Also called mayo, this dressing is one of the most popular condiments in the world. Its creamy texture and tangy flavor make it a great spread on sandwiches, an ingredient in dressings, or a base for salads such as chicken, tuna, or potato salad. 
Finding mayonnaise substitutes is relatively easy because the consistency is easy to mimic, even if the flavor is not. Because mayo is made with mostly vegetable oil, usually soybean or olive oil, and also contains eggs, it is not vegan, and also very high in fat and calories. Soy and egg are also common allergens, and since mayonnaise is made with raw egg, there is a chance of salmonella contamination as well. Fortunately, there are several amazing and simple mayonnaise substitutes such as Greek yogurt, avocado, hummus, pesto, olive oil, and vegan mayo among others.
Very closely mimicking the texture and tang of mayo, Greek yogurt can be used in place of mayonnaise in virtually any situation. Using reduced-fat or fat-free varieties makes this an even healthier option, but some people do find the acidity of Greek yogurt to be slightly more than they expect in certain dishes, so use in moderation. 
Mashed avocado is a good vegan mayo replacement on sandwiches, and can also be used in chicken or tuna salads. It is also packed with good antioxidants and healthy fats, making it one of the best replacement options.
This chickpea-based dip is also vegan and is a delicious spread. It generally has much less fat than mayonnaise as well, and comes in a variety of flavors, unlike mayonnaise. 
As a sandwich topping or as a salad base, this basil-based condiment will give dishes a different, but still delicious flavor when used instead of mayonnaise.
Using a little bit of olive oil in dressings or salads in place of mayo will result in a less creamy texture, but it eliminates the egg and can be a healthier option that still improves the consistency of a dish.
Many supermarkets, especially health-food or vegan stores, will carry egg-free versions of mayonnaise. While still somewhat high in fat, they have the same flavor and texture of mayo without using eggs.