This Chapter is devoted to the study of several Riccati-type differential equations, namely: \(\bullet \) jump matrix Riccati differential equations of stochastic control/filtering : such equations arise in connection with the solution of several optimal control/filtering problems for a large class of jump stochastic linear differential equation. \(\bullet \) jump matrix linear differential equation with Riccati-type jumping operator : such equations are related to some optimal control problems for a class of jump linear stochastic system controlled by impulses, i.e., the control actions take places only at the jump time instances. The above equations can be viewed as particular cases of a larger class of jump matrix nonlinear differential equations. In order to obtain the most general results, we shall systematically study such a general mathematical object without referring to any optimal control/filtering problem. The obtained results will then be specialized in a second step in order to cope with the Riccati-type equations cited above. We begin by analyzing the problem of the global existence on a whole given interval \([t_0,T]\) of a solution with given terminal values of a backward jump matrix nonlinear differential equation. Then, we shall study the problem of the existence on an unbounded interval \([t_0,\infty )\) of some particular solutions such as the maximal solution, the minimal solution and the stabilizing solution, respectively. We provide conditions which guarantee the existence and the uniqueness of such global solutions. The proofs are mainly based on positivity properties of linear evolution operators defined by the generalized Lyapunov differential equations with jumps studied in Chap. 2 . The last part of this chapter will be devoted to the numerical aspects of computing such global solutions for the considered jump Riccati-type differential equations. We shall provide Newton-like iterative algorithms and obtain the conditions that guarantee the global convergence of such numerical schemes.