SYNAPS (SYmbolic Numeric APplications) is a C++ library devoted to symbolic and numeric computations. It provides data-structures for the manipulation of basic algebraic objects, such as vectors, matrices (dense, sparse, structured), univariate and multivariate polynomials. It contains solvers for univariate and multivariate polynomials, including generalized normal form or subdivision solvers, tools for the manipulatiion of algebraic numbers, for the construction of resultants, ... In this talk, we will describe shortly its design, its main features and functionalities, show some applications in computational geometry for algebraic curves and surfaces and explain how it can be embbeded in an interpreter such as mathemagix or a modeling tool such as axel.