Microfluidic technologies have recently been shown to hold significant potential as novel tools for producing micro- and nano-scale structures for a variety of applications in tissue engineering and cell biology. Over the last decade, microfluidic spinning has emerged as an advanced method for fabricating fibers with diverse shapes and sizes without the use of complicated devices or facilities. In this critical review, we describe the current development of microfluidic-based spinning techniques for producing micro- and nano-scale fibers based on different solidification methods, platforms, geometries, or biomaterials. We also highlight the emerging applications of fibers as bottom-up scaffolds such as cell encapsulation or guidance for use in tissue engineering research and clinical practice.