Robotics is one of the core areas where the bioinspiration is frequently used to design various engineered morphologies and to develop novel behavioral controllers comparable to the humans and animals. Biopinspiration requires a solid understanding of the functions and concepts in nature and developing practical engineering applications. However, understanding these concepts, especially from a human or animal point of view, requires the signi cant use of mathematical modeling and system identi cation methods. In this thesis, we focus on developing new system identi cation methods for understanding legged locomotion models towards building better legged robot platforms that can locomote e ectively as their animal counterparts do in nature. In the rst part of this thesis, we present our e orts on experimental validation of the predictive performance of mechanics-based mathematical models on a physical one-legged hopping robot platform. We extend upon a recently proposed approximate analytical solution developed for the lossy spring{mass models for a real robotic system and perform a parametric system identi cation to carefully identify the system parameters in the proposed model. We also present our assessments on the predictive performance of the proposed approximate analytical solution on our one-legged hopping robot data. Experiments with di erent leg springs and cross validation of results yield that our approximate analytical solutions provide a su ciently accurate representation of the physical robot platform. In the second part, we adopt a data-driven approach to obtain an input{output representation of legged locomotion models around a stable periodic orbit (a.k.a. limit cycle). To this end, we rst linearize the hybrid dynamics of legged locomotor systems around a limit cycle to obtain a linear time periodic (LTP) system representation. Hence, we utilize the frequency domain analysis and identi cation methods for LTP systems towards the identi cation of input{output models (harmonic transfer functions) of legged locomotion. We propose simulation experiments on simple legged locomotion models to illustrate the prediction performance of the estimated input{output models. Finally, the third part considers estimating state space models of legged locomotion using input{output data. To accomplish this, we rst propose a state space identi cation method to estimate time periodic state and input matrices of a hybrid LTP system under full state measurement assumption. We then release this assumption and proceed with subspace identi cation methods to estimate LTP state space realizations for unknown stable LTP systems. We utilize bilinear (Tustin) transformation and frequency domain lifting methods to generalize our solutions to di erent LTP system models. Our results provide a basis towards identi cation of state space models for legged locomotion.