What are important limitations of JSON.stringify() and JSON.parse()?

Direct answer

JSON serialization supports JSON-compatible data, not arbitrary JavaScript object semantics; some values are omitted or transformed, BigInt and cycles need special handling, and prototypes/methods are not reconstructed by JSON.parse().

JSON is a data interchange format. Treating JSON.parse(JSON.stringify(value)) as a universal object clone loses information because JavaScript contains many values that JSON cannot represent directly.

undefined, functions, and symbols are not represented as normal object property values in the resulting JSON.
NaN and infinities serialize as null.
Date typically becomes a string through its JSON conversion behavior rather than remaining a Date object after parsing.
Map and Set do not automatically become their logical entries without custom conversion.
Cyclic object graphs throw unless you design a replacer/serialization scheme that handles references.
BigInt is not directly JSON-serializable without custom handling.

Use replacer/reviver functions or an application-specific schema when values need controlled conversion. For data interchange, explicit schemas are often more reliable than hoping arbitrary runtime objects round-trip.