Lattice structures offer many advantages in design and manufacturing, including high strength-to-weight ratios, increased surface area, and the ability to mimic the biological internal structures. Recent advances in additive manufacturing have enabled the fabrication of lattice structures with heterogenous and functionally graded materials. Among various representation methods, implicit forms have gained attention on realizing lattices because of their versatility in managing complex geometry and topology. This talk presents recent research on constructing conforming and heterogenous lattice structures--referred to as microstructures--using implicit representations. We explore the fabrication of these implicit form-based lattice structures via 3D printing and discuss methods to control the wall thickness of the microstructures. We first introduce a method to construct implicit form-based microstructures that conform to the macro-shape of freeform trivariate models. Each unit microstructure is defined by a precise implicit function or a spline trivariate, and populates a macro-shape represented in a trivariate parametric, resulting in conforming microstructures. The resulting microstructures can be functionally graded or heterogenous, with heterogeneity encoded either at the unit level or across the macro-shape. A novel slicing algorithm that does not employ piecewise linear approximations is also presented to preserve the precision of the implicit forms during 3D printing. The method is demonstrated through the 3D printing of microstructures in graded colors using various implicit functions. Next, we present a method to control the thickness of implicit form-based microstructures using variable offsets. Graded wall and edge thickness can be achieved either across the lattice or within individual microstructures by spatially varying offset distances to the implicit forms. We present algorithms for constructing implicit B-spline forms and computing both constant and variable offsets of the implicit B-splines, either in global or lattice space. These heterogeneous implicit form-based lattice structures can be analyzed using an immersive approach as well.