The Vue watch API is a powerful tool for tracking reactive data changes and performing operations when those changes occur. It can be used with either ref or reactive values, offering flexibility in how it's applied. The key to using the watch API effectively is understanding its nuances and behavior depending on the type of data being watched. For simple data types like numbers, strings, and booleans, watching a single ref involves passing the ref as the first argument to the watch API with a callback function that applies side effects to the data. However, when dealing with complex data types like arrays and objects, additional considerations are necessary. To deeply watch nested arrays and objects, a deep copy of values may be required, using utility functions like lodash.cloneDeep. Additionally, watching multiple refs can be achieved by passing an array of refs to the watch API. The watch API also offers an optional third argument, "deep," which extends its functionality to keep track of deeply nested values. When watching reactive objects or arrays, it's often recommended to use lodash to ensure tracking both previous and current values.