There are two main ways to render blocks and items dynamically, depending on what you want to do.
Custom Models can be used to dynamically render the block when the chunk mesh is rebuilt. This means that the model will be re-generated only when the chunk is updated, or when you force it to update.
Block Entity Renderers are called every frame to draw whatever you want, but the model will still be rendered. This can be used on top of the Custom Models for animation, e.g. a chest opening animation.