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Nonlinear dynamics of an optical pulse or a beam continue to be one of theactive areas of research in the field of optical solitons. Especially, inmulti-mode fibers or fiber arrays and photorefractive materials, the vectorsolitons display rich nonlinear phenomena. Due to their fascinating andintriguing novel properties, the theory of optical vector solitons has beendeveloped considerably both from theoretical and experimental points of viewleading to soliton based promising potential applications. In the recent past,many types of vector solitons have been identified both in the integrable andnon-integrable coupled nonlinear Schr\"{o}dinger (CNLS) equations framework. Inthis article, we review some of the recent progress in understanding thedynamics of the so called nondegenerate vector bright solitons in nonlinearoptics, where the fundamental soliton can have more than one propagationconstant. We address this theme by considering the integrable two CNLS familyof equations, namely Manakov system, mixed 2-CNLS system, coherently CNLSsystem, generalized CNLS system and two-component long-wave short-waveresonance interaction (LSRI) system. In these models, we discuss the existenceof nondegenerate vector solitons and their associated novel multi-humpgeometrical profile nature by deriving their analytical forms through theHirota bilinear method. Then we reveal the novel collision properties of thenondegenerate solitons in the Manakov system as an example. The asymptoticanalysis shows that the nondegenerate solitons, in general, undergo three typesof elastic collisions without any energy redistribution among the modes.Further, we show that the energy sharing collision exhibiting vector solitonsarises as a special case of the newly reported nondegenerate vector solitons.Finally, we point out the possible further developments in this subject andpotential applications.

Nondegenerate bright solitons in coupled nonlinear Schr\"{o}dinger systems: Recent developments on optical vector solitons