  Optimal control problems of forward stochastic Volterra integral equations
(SVIEs) are formulated and studied. When control region is arbitrary subset of
Euclidean space and control enters into the diffusion, necessary conditions of
Pontryagin's type for optimal controls are established via spike variation. Our
conclusions naturally cover the analogue of stochastic differential equations
(SDEs), and our developed methodology drops the reliance on It\^o formula and
second-order adjoint equations. Some new features, that are concealed in the
SDEs framework, are revealed in our situation. For example, instead of using
second-order adjoint equations, it is more appropriate to introduce
second-order adjoint processes. Moreover, the conventional way of using one
second-order adjoint equation is inadequate here. In other words, two adjoint
processes, which just merge into the solution of second-order adjoint equation
in SDEs situation, are actually required and proposed in our setting.
