Using intricate but elementary calculations, the author obtains characterizations of Lie isomorphisms, Lie derivations, and other mappings of prime rings which extend a number of results in the literature. For the statement of all the results which follow, \(R\) and \(A\) are prime rings with neither of characteristic two and neither embedding in \(M_ 2(K)\) for \(K\) a field. The extended centroid of \(R\) is denoted by \(C(R)=C\), and \([x,y]=xy-yx\). The main results are: Theorem 1. If \(f: R\times R\to R\) is biadditive and \([f(x,x),x]=0\) for all \(x\in R\), then \(f(x,x) =\lambda x^ 2+ \mu(x)x+ \nu(x)\) for \(\lambda\in C\) and \(\mu,\nu:R\to C\) with \(\mu\) additive; Theorem 2. Let \(R\) and \(A\) be centrally closed algebras over the field \(F\neq GF(3)\), and \(\theta: R\to A\) a bijective \(F\)-linear map satisfying \([\theta(x^ 2), \theta(x)]=0\) for all \(x\in R\). Then \(\theta(x)= cg(x)+ h(x)\) with \(c\in F-\{0\}\), \(g,h: R\to A\), \(g\) is an isomorphism or anti-isomorphism onto \(A\), and \(h(R)\) is central; Theorem 3. If \(\theta: R\to A\) is a Lie isomorphism (\(\theta([x,y])= [\theta(x),\theta(y)]\)), then \(\theta= \varphi+\tau\) where \(\varphi: R\to AC(A)\), \(\varphi\) is a monomorphism or the negative of an anti-monomorphism, and \(\tau: R\to C(A)\) with \(\tau([R,R])=0\); and last, Theorem 4. If \(D\) is a Lie derivation of \(R\) (\(D([x,y])= [D(x),y]+ [x,D(y)]\)), then \(D= \delta+\gamma\) where \(\delta: R\to RC(R)\) is a derivation, and \(\gamma: R\to C\) is additive with \(\gamma([R,R]) =0\).