Handwriting Recognition Technology has been improving much under the purview of pattern recognition and image processing since a few decades. This paper focuses on the comprehensive survey on on-line handwriting recognition system along with the real application by taking Nepali natural handwriting (a real example of one of the cursive handwritings). The survey mainly includes pre-processing, feature vector and similarity measures in between the non-linear 2D sequences of coordinates, and their effective applications. A very highlighting topic ``Dynamic Time Warping Algorithm'' (DTW) is introduced, which has been popular in determining the distance between two non-linear sequences ranging from handwriting to speech recognition. Besides these contemporary research issues/areas, stroke number and order free Nepalese natural handwritten recognition system is presented in the second step. Writing one's own style brings unevenness in writing units, which is the most difficult part to classify. Writing units reveal number, shape, size, order of stroke, and speed in writing. Variation in the number of strokes, their order, shapes and sizes, tilting angles and similarities among characters from one another are the important factors, which are to be considered in classification for Nepali. This paper utilizes structural properties of those alphanumeric characters, which have variable writing units. It uses a string of pen tip's positions and tangent angles of every consecutive point as a feature vector sequence of a stroke. We constructed a prototype recognizer that uses the DTW algorithm to align handwritten strokes with stored strokes' templates and determine their similarity. Separate system is trained for original and preprocessed writing samples and achieved recognition rates of 85.87% and 88.59% respectively. This introduces novel real time handwriting recognition on Nepalese alphanumeric characters, which are independent of number of strokes, as well as their order.